# Patent

## Title
Multiple input multiple output communication system using codebook corresponding to each reporting mode

## Abstract

A multiple input multiple output (MIMO) communication system using a first codebook and a second codebook is provided. The first codebook and the second codebook may independently exist, or may exist in a form of an overall codebook in which the first codebook and the second codebook are integrated with each other. A receiver may extract a first precoding matrix indicator from the first codebook, and may extract a second precoding matrix indicator from the second codebook. The receiver may also extract the first precoding matrix indicator and the second precoding matrix indicator from the overall codebook. The first precoding matrix indicator and the second precoding matrix indicator may be fed back to a transmitter. The transmitter may determine a precoding matrix based on the first precoding matrix indicator and the second precoding matrix indicator.

## Background
CROSS-REFERENCE TO RELATED APPLICATION(S)
This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 61/329,634, filed on Apr. 30, 2010, U.S. Provisional Application No. 61/355,681, filed on Jun. 17, 2010, U.S. Provisional Application No. 61/356,768, filed on Jun. 21, 2010, U.S. Provisional Application No. 61/373,942, filed on Aug. 16, 2010, U.S. Provisional Application No. 61/388,736, filed on Oct. 1, 2010, and U.S. Provisional Application No. 61/428,348, filed on Dec. 30, 2010, all of which were filed in the United States Patent and Trademark Office, and claims the benefit under 35 U.S.C. §119(a) of Korean Patent Application No. 10-2011-0031200, filed on Apr. 5, 2011, in the Korean Intellectual Property Office, the entire disclosures of which are incorporated herein by reference for all purposes.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The following description relates to a multiple input multiple output (MIMO) communication system using a codebook, and more particularly, to codebooks corresponding to respective reporting modes used by a transmitter and a receiver included in a MIMO communication system.
2. Description of the Related Art
A multiple input multiple output (MIMO) communication system may include a transmitter and at least one receiver. For example, the MIMO communication system may include a base station and at least one terminal. In a downlink, the base station may perform a functionality as the transmitter, and each of the at least one terminal may perform a functionality as the receiver.
The transmitter or the receiver operating in the MIMO communication system may include a plurality of antennas, and may transmit and receive data using the plurality of antennas. A wireless channel may be formed between each transmit antenna of the transmitter and each receive antenna of the receiver. The transmitter and the receiver may share information associated with the wireless channel, thereby achieving a high data rate.
In a closed-loop MIMO communication system, feedback information to be shared between the transmitter and the receiver may include a rank indicator indicating a preferred rank of the receiver, a precoding matrix indicator indicating a preferred precoding matrix, channel quality information indicating a quality of a wireless channel, and the like. The receiver may select one of matrices or vectors included in a codebook using a predefined codebook, and may feed back an index of the selected matrix or vector as the precoding matrix indicator.
SUMMARY OF THE INVENTION
In one general aspect, there is provided a communication method of a receiver in a multiple input multiple output (MIMO) communication system including a transmitter having eight transmit antennas and the receiver, the communication method including extracting a first precoding matrix indicator corresponding to a first codeword included in a first codebook and a second precoding matrix indicator corresponding to a second codeword included in a second codebook, and transmitting, to the transmitter, the first precoding matrix indicator and the second precoding matrix indicator.
In another general aspect, there is provided a communication method of a receiver in a MIMO communication system including a transmitter having eight transmit antennas and the receiver, the communication method including feeding back, to the transmitter, a first precoding matrix indicator corresponding to a first codeword included in a first codebook in order to indicate a recommended precoding matrix at a first reporting point in time, and feeding back, to the transmitter, a second precoding matrix indicator corresponding to a second codeword included in a second codebook in order to indicate a recommended precoding matrix at a second reporting point in time.
In still another general aspect, there is provided a communication method of a transmitter in a MIMO communication system including the transmitter having eight transmit antennas and a receiver, the communication method including receiving, from the receiver, a first precoding matrix indicator corresponding to a first codeword included in a first codebook and a second precoding matrix indicator corresponding to a second codeword included in a second codebook, accessing a memory that stores the first codebook and the second codebook, and generating a precoding matrix using the first precoding matrix indicator and the second precoding matrix indicator.
In yet another general aspect, there is provided a communication method of a transmitter in a MIMO communication system including the transmitter having eight transmit antennas and a receiver, the communication method including receiving, from the receiver, a first precoding matrix indicator corresponding to a first codeword included in a first codebook, the first precoding matrix indicator indicating a recommended precoding matrix at a first reporting point in time, receiving, from the receiver, a second precoding matrix indicator corresponding to a second codeword included in a second codebook, the second precoding matrix indicator indicating a recommended precoding matrix at a second reporting point in time, accessing a memory that stores the second codebook, and generating the recommended precoding matrix at the second reporting point in time using the second precoding matrix indicator received at the second reporting point in time.
Other features and aspects may be apparent from the following detailed description, the drawings, and the claims.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram illustrating an example of a multiple input multiple output (MIMO) communication system.
FIG. 2 is a diagram illustrating an example of a communication method of a receiver and a transmitter that share channel information using a single codebook.
FIG. 3 is a diagram illustrating an example of a relationship between two codebooks and a precoding matrix.
FIG. 4 is a diagram illustrating an example of a communication method of a receiver and a transmitter that share channel information using two codebooks.
FIG. 5 is a diagram illustrating an example of a communication method of a receiver and a transmitter that operate in a physical uplink control channel (PUCCH) 1-1 sub-mode 2.
FIG. 6 is a diagram illustrating an example of a communication method of a receiver and a transmitter that operate in PUCCH 2-1 sub-modes 1 and 2.



Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals should be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience.
DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS
The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. Accordingly, various changes, modifications, and equivalents of the methods, apparatuses, and/or systems described herein may be suggested to those of ordinary skill in the art. Also, description of well-known functions and constructions may be omitted for increased clarity and conciseness.
Hereinafter, embodiments will be described in detail with reference to the accompanying drawings.
FIG. 1 illustrates an example of a multiple input multiple output (MIMO) communication system.
Referring to FIG. 1, the MIMO communication system may include a transmitter 110 and a plurality of receivers 120, 130, and 140.
Nt transmit antennas may be installed in the transmitter 110. The transmitter 110 may function as a base station in a downlink, and may function as a terminal in an uplink. Nr receive antennas may be installed in the receivers 120, 130, and 140. Each of the receivers 120, 130, and 140 may function as a terminal in the downlink, and may function as a base station in the uplink. Hereinafter, embodiments will be described based on an operation of the transmitter 110 and the receivers 120, 130, and 140 in the downlink. The embodiments may be applicable to the uplink.
Channels may be formed between the transmitter 110 and the receivers 120, 130, and 140. Data may be transmitted from the transmitter 110 to the receivers 120, 130, and 140 via the channels. The transmitter 110 may precode at least one data stream using a precoding matrix, enhancing a performance of the MIMO communication system. A data stream may also be referred to as data.
The transmitter 110 may generate or determine a more accurate precoding matrix by verifying information associated with channel direction and information associated with channel quality. Information associated with the channel direction and information associated with the channel quality may be one example of channel information. Information associated with the channel direction may include a precoding matrix indicator.
For example, the transmitter 110 and the receivers 120, 130, and 140 may share the precoding matrix indicator using a codebook. The codebook may include a plurality of codewords. Each of the plurality of codewords may correspond to a vector or a matrix. A size of the codebook may correspond to a number of codewords. For example, a 3-bit codebook may include eight codewords, and a 4-bit codebook may include 16 codewords.
Each of the receivers 120, 130, and 140 may select a single codeword from the plurality of codewords, and may generate an indicator of the selected codeword as a precoding matrix indicator. The precoding matrix indicator may be fed back to the transmitter 110. The transmitter 110 may verify a codeword indicated by the precoding matrix indicator, using the codebook. The transmitter 110 may generate or determine an optimal precoding matrix based on the codeword corresponding to the precoding matrix indicator.
A dimension of a precoding matrix may be dependent on a rank of the transmitter 110. The rank of the transmitter 110 may correspond to a number of data streams desired to be transmitted or a number of layers of the transmitter 110.
FIG. 2 illustrates an example of a communication method of a receiver and a transmitter that share channel information using a single codebook.
Referring to FIG. 2, at 210, the transmitter may transmit a well-known signal to the receiver. The well-known signal may be a pilot signal.
At 220, the receiver may estimate a channel formed from the transmitter to the receiver based on the well-known signal.
At 230, the receiver may select, from a codebook, a codeword suitable for the estimated channel and generate a precoding matrix indicator including an index of the selected codeword. In this example, the same codebook may be stored in both the transmitter and the receiver.
At 240, the receiver may feed back a precoding matrix indicator to the transmitter. The receiver may also feed back channel quality information and a rank indicator.
At 250, the transmitter may generate or determine an optimal precoding matrix based on the fed back precoding matrix indicator. At 260, the transmitter may transmit data using the precoding matrix.
The communication method of the transmitter and the receiver when the transmitter and the receiver use the same single codebook is described above with reference to FIG. 2. According to embodiments, two codebooks may be used for the receiver and the transmitter to share two precoding matrix indicators.
Hereinafter, it is assumed that a first codebook C1 and a second codebook C2 are present, and two codebooks are stored in the receiver and the transmitter, respectively. It is also assumed that a precoding matrix W is finally recommended by the receiver and is used by the transmitter.
FIG. 3 illustrates an example of a relationship between two codebooks and a precoding matrix.
Referring to FIG. 3, both a transmitter and a receiver may store a first codebook C1 310 and a second codebook C2 320. The receiver may select a preferred first codeword W1 from the first codebook C1 310, and may select a preferred second codeword W2 from the second codebook C2 320. A first precoding matrix indicator may be fed back to the transmitter as an index of the preferred first codeword W1, and a second precoding matrix indicator may be fed back to the transmitter as an index of the preferred second codeword W2.
Based on the first precoding matrix indicator and the second precoding matrix indicator, the transmitter may find the preferred first codeword W1 from the first codebook C1 310, and may find the preferred second codeword W2 from the second codebook C2 320. The transmitter may determine a precoding matrix W=f(W1, W2) based on the preferred first codeword W1 and the preferred second codeword W2.
In W=f(W1, W2), a function f may be variously defined. For example, W=f(W1, W2)=W2W1 or W=f(W1, W2)=W1W2 may be defined.
W1 corresponds to the preferred first codeword of the receiver corresponding to the first precoding matrix indicator selected by the receiver from the first codebook C1. W2 corresponds to the preferred second codeword of the receiver corresponding to the second precoding matrix indicator of the receiver selected from the second codebook C2. The first codebook C1 or the first precoding matrix indicator may be used to indicate a property of a channel in a wideband including a plurality of subbands, or to indicate a long-term property of the channel. The second codebook C2 or the second precoding matrix indicator may be used to indicate a property of a channel in a subband or to indicate a short-term property of the channel.
In W=f(W1, W2)=W2W1, W may have a dimension of Nt×R and W1 may have a dimension of Nt×R. W2 may have a dimension of Nt×Nt. In W=f(W1, W2)=W1W2, W may have a dimension of Nt×R and W1 and W2 may have a variety of dimensions based on R. Here, R corresponds to a rank and indicates a number of data streams or a number of layers.
Hereinafter, the first codebook C1 including candidates of W1 and the second codebook C2 including candidates of W2 when the transmitter includes eight transmit antennas will be defined with respect to each of various ranks. Since W1 is indicated by a combination of W1 and W2, to define the candidates of W1 and the candidates of W2 may be equivalent to define candidates of W. In addition to the first codebook C1 and the second codebook C2, the candidates of W may also be defined.
Design of rank 1 codebook when the transmitter includes eight transmit antennas:
In dual polarized channels, a precoding matrix in one subband may be expressed by,




  W
  =
  
    
      
        2
      
      2
    
    ⁡
    
      [
      
        
          
            
              
                
                  2
                  -
                  
                    
                      
                      α
                      
                    
                    2
                  
                
              
              ⁢
              A
            
          
        
        
          
            
              α
              ⁢
              
                
              
              ⁢
              B
            
          
        
      
      ]
    
  




A and B may correspond to unit norm vectors having a dimension of Nt/2×1 and may independently perform beamforming in each polarization. Each polarization may appear as an effectively single antenna after beamforming is performed in each polarization using A and B. To design codebooks with respect to A and B may be dependent on statistical properties of a channel in each polarization. Without further assumption with respect to properties, A and B may account for subband/short-term information and wideband/long-term information.
Beamforming of polarizations may be performed by vector




  
    [
    
      
        
          
            
              2
              -
              
                
                  
                  α
                  
                
                2
              
            
          
        
      
      
        
          α
        
      
    
    ]
  
  .




Here, α corresponds to a complex scalar and may account for a phase difference and a magnitude difference. The phase difference between the polarizations may typically correspond to a short-term property and the magnitude difference may correspond to a function of the subband/short-term property and wideband/long-term property. A cross-polarization discrimination factor is generally referred to as XPD of a channel. XPD indicates a wideband/long-term property of a dual polarization channel and a mean value with respect to α may vary.

In general, A and B may be selected to be different from each other. However, when an interval between antennas is relatively close and each angle spread is relatively low, a beamforming vector with respect to a first polarization and a beamforming vector with respect to a second polarization may be regarded to be identical to each other. Since beamforming is invariant over a phase shift, B=ejφA may be established. Here, a selection of φ may not affect the performance of the dual polarization channel. When the interval between antennas is close, A, B, and φ may be associated with wideband/long-term properties of a channel. Accordingly, a precoding matrix in a subband may be expressed by,




  W
  =
  
    
      
        
          2
        
        2
      
      ⁡
      
        [
        
          
            
              
                
                  
                    2
                    -
                    
                      
                        
                        α
                        
                      
                      2
                    
                  
                
                ⁢
                A
              
            
          
          
            
              
                α
                ⁢
                
                  
                
                ⁢
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  




For an appropriate design of A, discrete Fourier transformation (DFT) vectors may be used. In the above equation, a last equal mark may remind a structure of W2W1. A subband/short-term matrix may be expressed by




  
    W
    2
  
  =
  
    [
    
      
        
          
            
              
                2
                -
                
                  
                    
                    α
                    
                  
                  2
                
              
            
            ⁢
            
              I
              
                
                  n
                  t
                
                /
                2
              
            
          
        
        
          
            
          
        
      
      
        
          
            
          
        
        
          
            α
            ⁢
            
              
            
            ⁢
            
              I
              
                
                  n
                  t
                
                /
                2
              
            
          
        
      
    
    ]
  




A wideband/long-term matrix may be expressed by




  
    W
    1
  
  =
  
    
      
        2
      
      2
    
    ⁡
    
      [
      
        
          
            A
          
        
        
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              A
            
          
        
      
      ]
    
  




In a special case where ejφ=1:




  
    
      
        W
        ⁢
        
          =
          
            (
            a
            )
          
        
        ⁢
        
        ⁢
        
          
            
              
                2
              
              2
            
            ⁡
            
              [
              
                
                  
                    
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  A
                
              
              
                
                  A
                
              
            
            ]
          
        
      
    
  
  
    
      
        
          =
          
            (
            b
            )
          
        
        ⁢
        
        ⁢
        
          
            
              
                2
              
              2
            
            ⁡
            
              [
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                  
                
                
                  
                    α
                  
                
              
              ]
            
          
          ⊗
          A
        
      
    
  
  
    
      
        
          =
          
            (
            c
            )
          
        
        ⁢
        
        ⁢
        
          
            
              
                2
              
              2
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    A
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                
              
              
                
                  α
                
              
            
            ]
          
        
      
    
  




As shown in the above equation, in the special case where ejφ=1, many equivalent methods may be used to express the same precoding matrix. For example, in the above equation, (a) corresponds to a method of using the structure of W2W1, (b) corresponds to a method of using Kronecker product, and (c) corresponds to a method of using a structure of W1W2.
When the interval between antennas is close, the precoding matrix may be expressed using the aforementioned equations in a single polarization channel. In this example, α=1, a value of φ may be A-dependent and be selected to obtain DFT vectors for eight transmit antennas. For example, W2 may correspond to an identity matrix and W1 may provide a wideband precoding matrix of DFT vectors. Contrast to dual polarization channels, the selection of φ may affect the performance of single polarization channels.
According to the structure of W2W1 shown in




  
    W
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                  ⁢
                  A
                
              
            
            
              
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  A
                
              
            
          
          ]
        
      
      =
      
        
          
            
              2
            
            2
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
              
            
            ]
          
        
        ⁡
        
          [
          
            
              
                A
              
            
            
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  A
                
              
            
          
          ]
        
      
    
  
  ,




the wideband/long-term matrix





   
  
    [
    
      
        
          A
        
      
      
        
          
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                φ
              
            
            ⁢
            A
          
        
      
    
    ]
  




may have a significantly robust physical meaning That is, in its given Nt×1 dimension, the wideband/long-term matrix may be equivalent to a rank and thus, may provide a direct insight to a rank 1 wideband PMI structure. Also, in the aforementioned W2W1 structure, a structure





   
  
    [
    
      
        
          A
        
        
          
            
          
        
      
      
        
          
            
          
        
        
          A
        
      
    
    ]
  




may not be associated with the rank and may not provide any information associated with a wideband PMI structure.

A full utilization of power amplifiers may be used as an important design criterion. When only a phase shift keying (PSK) is used to decrease the complexity of PMI search, there is a need to constrain a precoding matrix. It may be assumed that the precoding matrix becomes constant modulus and |α|=1. In this scenario, α may use a subband/long-term property with respect to a phase shift between polarizations.
Design of rank 2 codebook when the transmitter includes eight transmit antennas:
A rank 2 precoding matrix may include two orthogonal columns, which may be expressed by



  
    
      W
      
        (
        1
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          
                            α
                            1
                          
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  
                    α
                    1
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              
                A
                1
              
            
          
          
            
              
                B
                1
              
            
          
        
        ]
      
    
  




  
    
      W
      
        (
        2
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          
                            α
                            2
                          
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  
                    α
                    2
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              
                A
                2
              
            
          
          
            
              
                B
                2
              
            
          
        
        ]
      
    
  



The full utilization of power in each antenna may force |α1|2+|α2|2=2, and may establish α2=√{square root over (2−|α|2)}ejδ with α1=α. In this example, the following equations may be expressed.



  
    
      W
      
        (
        1
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              
                A
                1
              
            
          
          
            
              
                B
                1
              
            
          
        
        ]
      
    
  




  
    
      W
      
        (
        2
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                    α
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      δ
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              
                A
                2
              
            
          
          
            
              
                B
                2
              
            
          
        
        ]
      
    
  



To obtain mutually orthogonal columns, A1HA2=0 and B1HB2=0 may be sufficient. A1, A2, B1, and B2 may be approximated by two dominant eigenvectors of Nt×Nt covariance matrix. Many combinations may be used for design of the precoding matrix, which may cause great overheard. In a scenario with a narrow interval between antennas, A1=A, A2=A, B1=ejφ1A, and B2=ejφ2A. A cross-polarized setup may help achievement of rank 2 transmission in a configuration where the interval between antennas is narrow.
Parameters φ1 and φ2 may be selected to guarantee so that W(1) and W(2) may be orthogonal with respect to each other. In this example, φ1=φ, and φ2=φ+π. The rank 2 precoding matrix may be expressed by




  
    
      
        W
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      
                      α
                      
                    
                    ⁢
                    A
                  
                
              
              
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      -
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        δ
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
              
            
            ]
          
        
      
    
  




The precoding matrix may be expressed using the W2W1 structure, as follows:




  
    
      
        W
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      
                      α
                      
                    
                    ⁢
                    A
                  
                
              
              
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      -
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        δ
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            
              1
              2
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                      ⁢
                      A
                    
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                
                
                  
                    
                    α
                    
                  
                
              
              
                
                  α
                
                
                  
                    
                      -
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        δ
                      
                    
                  
                
              
            
            ]
          
        
      
    
  




In this equation,



  
    
      W
      1
    
    =
    
      [
      
        
          
            A
          
          
            
              
            
          
        
        
          
            
              
            
          
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              A
            
          
        
      
      ]
    
  




  and




  
    
      W
      2
    
    =
    
      
        
          1
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    2
                    -
                    
                      
                        
                        α
                        
                      
                      2
                    
                  
                
              
              
                
                  
                  α
                  
                
              
            
            
              
                α
              
              
                
                  
                    -
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                  
                  ⁢
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      δ
                    
                  
                
              
            
          
          ]
        
      
      .
    
  



The precoding matrix may be expressed using a variety of methods. For example, the precoding matrix may be expressed by




  
    
      
        W
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            1
            2
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      
                      α
                      
                    
                    ⁢
                    A
                  
                
              
              
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      -
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        δ
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            [
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          α
                          
                        
                        2
                      
                    
                  
                
                
                  
                    
                    α
                    
                  
                
              
              
                
                  α
                
                
                  
                    
                      -
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                    ⁢
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        δ
                      
                    
                  
                
              
            
            ]
          
          ∘
          
            [
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      A
                    
                    
                      
                        
                          
                        
                        ⁢
                        A
                      
                    
                  
                  
                    
                      
                        
                          
                        
                        ⁢
                        
                          
                            e
                            
                              j
                              ⁢
                              
                                
                              
                              ⁢
                              φ
                            
                          
                          ⁢
                          A
                        
                      
                    
                    
                      
                        
                          -
                          
                            e
                            
                              j
                              ⁢
                              
                                
                              
                              ⁢
                              φ
                            
                          
                        
                        ⁢
                        A
                      
                    
                  
                
                ]
              
            
            ]
          
        
      
    
  




In this equation, ∘ corresponds to Hardmard product, and



  
    
      
        W
        1
      
      =
      
        
          1
          2
        
        ⁡
        
          [
          
            
              
                A
              
              
                
                  
                    
                  
                  ⁢
                  A
                
              
            
            
              
                
                  
                    
                  
                  ⁢
                  
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
              
              
                
                  
                    -
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                  
                  ⁢
                  A
                
              
            
          
          ]
        
      
    
    ,
    
      

    
    ⁢
    and
  




  
    
      W
      2
    
    =
    
      
        
          1
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    2
                    -
                    
                      
                        
                        α
                        
                      
                      2
                    
                  
                
              
              
                
                  
                  α
                  
                
              
            
            
              
                α
              
              
                
                  
                    -
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                  
                  ⁢
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      δ
                    
                  
                
              
            
          
          ]
        
      
      .
    
  



When |α|=1 is assumed to maintain the precoding matrix as constant modulus, and to maintain a PSK alphabet, the rank 2 precoding matrix may include two orthogonal columns W(1) and W(2). Each column may satisfy the structure of the rank 1 precoding matrix, for example, as follows:



  
    
      W
      
        (
        1
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          
                            α
                            1
                          
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      φ
                      1
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  




  
    
      W
      
        (
        2
        )
      
    
    =
    
      
        
          
            2
          
          2
        
        ⁡
        
          [
          
            
              
                
                  
                    
                      2
                      -
                      
                        
                          
                          
                            α
                            2
                          
                          
                        
                        2
                      
                    
                  
                  ⁢
                  
                    I
                    
                      
                        n
                        t
                      
                      /
                      2
                    
                  
                
              
              
                
                  
                
              
            
            
              
                
                  
                
              
              
                
                  αI
                  
                    
                      n
                      t
                    
                    /
                    2
                  
                
              
            
          
          ]
        
      
      ⁡
      
        [
        
          
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      φ
                      2
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  



Two rank 1 precoding matrices may be differentiated using only the parameter φ. The parameters φ1 and φ2 may be selected to guarantee that W(1) and W(2) are orthogonal to each other. When φ1=φ and φ2=φ+π, the rank 2 precoding matrix may be expressed by




  
    
      
        W
        =
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          
                            2
                            -
                            
                              
                                
                                α
                                
                              
                              2
                            
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                    
                      
                        
                      
                    
                  
                  
                    
                      
                        
                      
                    
                    
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                  
                
                ]
              
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    
                      
                        
                      
                      ⁢
                      A
                    
                  
                
                
                  
                    
                      
                        
                      
                      ⁢
                      
                        
                          e
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            φ
                          
                        
                        ⁢
                        A
                      
                    
                  
                  
                    
                      
                        -
                        
                          e
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            φ
                          
                        
                      
                      ⁢
                      A
                    
                  
                
              
              ]
            
          
          .
        
      
    
  




Wideband/long-term matrix W1 may correspond to a wideband precoding matrix and may be given as




  
    W
    1
  
  =
  
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              A
            
            
              
                
                  
                
                ⁢
                A
              
            
          
          
            
              
                
                  
                
                ⁢
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  A
                
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
    .
  




A subband matrix W2 may be expressed by




  
    W
    2
  
  =
  
    
      [
      
        
          
            
              
                
                  2
                  -
                  
                    
                      
                      α
                      
                    
                    2
                  
                
              
              ⁢
              
                I
                
                  
                    n
                    t
                  
                  /
                  2
                
              
            
          
          
            
              
            
          
        
        
          
            
              
            
          
          
            
              α
              ⁢
              
                
              
              ⁢
              
                I
                
                  
                    n
                    t
                  
                  /
                  2
                
              
            
          
        
      
      ]
    
    .
  




The selection of φ may not affect the performance of the wideband precoding matrix W1 in dual polarization channels, however, may have a strong influence in single polarization channels. The parameter φ may be selected so that W1 may have excellent performance even in single polarization channels.
In a special case where ejφ=1:




  
    
      
        W
        ⁢
        
          =
          
            (
            a
            )
          
        
        ⁢
        
        ⁢
        
          
            
              1
              2
            
            ⁡
            
              [
              
                
                  
                    
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  A
                
                
                  
                    
                      
                    
                    ⁢
                    A
                  
                
              
              
                
                  
                    
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    -
                    A
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        
          =
          
            (
            b
            )
          
        
        ⁢
        
        ⁢
        
          
            
              
                2
              
              2
            
            ⁡
            
              [
              
                
                  
                    
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                
              
              ]
            
          
          ⁢
          
            
              U
              rot
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                
                  
                    0
                  
                  
                    A
                  
                
              
              ]
            
          
        
      
    
  
  
    
      
        
          =
          
            (
            c
            )
          
        
        ⁢
        
        ⁢
        
          
            
              1
              2
            
            ⁡
            
              [
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                  
                  
                    
                      
                        
                      
                      ⁢
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                  
                
                
                  
                    
                      α
                      ⁢
                      
                        
                      
                    
                  
                  
                    
                      
                        -
                        α
                      
                      ⁢
                      
                        
                      
                    
                  
                
              
              ]
            
          
          ⊗
          A
        
      
    
  
  
    
      
        
          =
          
            (
            d
            )
          
        
        ⁢
        
        ⁢
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      A
                    
                    
                      
                        
                      
                    
                  
                  
                    
                      
                        
                      
                    
                    
                      A
                    
                  
                
                ]
              
            
            ⁡
            
              [
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                  
                  
                    
                      
                        
                      
                      ⁢
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                    
                  
                
                
                  
                    
                      α
                      ⁢
                      
                        
                      
                    
                  
                  
                    
                      
                        -
                        α
                      
                      ⁢
                      
                        
                      
                    
                  
                
              
              ]
            
          
          .
        
      
    
  




In the special case where ejφ=1, many equivalent methods may be used to express the same precoding matrix. For example, in the above equation, (a) corresponds to a method of using the structure of W2W1, (b) corresponds to a method of using a rotated block diagonal structure, (c) corresponds to a method of using Kronecker product, and (d) corresponds to a method of using the structure of W1W2.
Design of Rank 3 Codebook When the Transmitter Includes Eight Transmit Antennas:
A rank 3 precoding matrix may be obtained by simply extending a structure induced with respect to the rank 1 precoding matrix and the rank 2 precoding matrix. By adding, to the rank 2 precoding matrix, a column orthogonal to the rank 2 precoding matrix, the rank 3 precoding matrix may be obtained as follows:



  
    
      
        
          W
          =
          
            
              1
              
                3
              
            
            ⁡
            
              [
              
                
                  
                    
                      W
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        3
                        )
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          =
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          
                            2
                            -
                            
                              
                                
                                α
                                
                              
                              2
                            
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                    
                      
                        
                      
                    
                  
                  
                    
                      
                        
                      
                    
                    
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                  
                
                ]
              
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    A
                  
                  
                    B
                  
                
                
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                      ⁢
                      A
                    
                  
                  
                    
                      
                        -
                        
                          e
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            φ
                          
                        
                      
                      ⁢
                      A
                    
                  
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                      ⁢
                      B
                    
                  
                
              
              ]
            
          
        
      
    
  




  or




  
    
      
        
          W
          =
          
            
              1
              
                3
              
            
            ⁡
            
              [
              
                
                  
                    
                      W
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        3
                        )
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          =
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          
                            2
                            -
                            
                              
                                
                                α
                                
                              
                              2
                            
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                    
                      
                        
                      
                    
                  
                  
                    
                      
                        
                      
                    
                    
                      
                        α
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            
                              n
                              t
                            
                            /
                            2
                          
                        
                      
                    
                  
                
                ]
              
            
            ⁡
            
              [
              
                
                  
                    A
                  
                  
                    A
                  
                  
                    B
                  
                
                
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                      ⁢
                      A
                    
                  
                  
                    
                      
                        -
                        
                          e
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            φ
                          
                        
                      
                      ⁢
                      A
                    
                  
                  
                    
                      
                        -
                        
                          e
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            φ
                          
                        
                      
                      ⁢
                      B
                    
                  
                
              
              ]
            
          
        
      
    
  



In this example, A and B may be orthogonal to each other.
Design of Rank 4 Codebook When the Transmitter Includes Eight Transmit Antennas:
Similarly with respect to rank 4, a rank 4 precoding matrix may be expressed using two rank 2 precoding matrices as follows:




  
    
      
        W
        =
        
        ⁢
        
          
            1
            
              4
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
                
                  
                    
                      
                        
                          W
                          
                            (
                            3
                            )
                          
                        
                      
                      
                        
                          W
                          
                            (
                            4
                            )
                          
                        
                      
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            1
            
              
                4
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        
        ⁢
        
          [
          
            
              
                A
              
              
                A
              
              
                B
              
              
                B
              
            
            
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  A
                
              
              
                
                  
                    -
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                  
                  ⁢
                  A
                
              
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  B
                
              
              
                
                  
                    -
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                  
                  ⁢
                  B
                
              
            
          
          ]
        
      
    
  




In this example, A and B may be orthogonal to each other.
Design of Rank r Codebook When the Transmitter Includes Eight Transmit Antennas:
With respect to rank r codebook, the precoding matrix may be expressed as follows:
When r is an odd number,



  
    
      
        
          W
          =
          
          ⁢
          
            
              1
              
                r
              
            
            ⁡
            
              [
              
                
                  
                    
                      W
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      
                        
                          ...
                        
                        
                          
                            W
                            
                              (
                              r
                              )
                            
                          
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          =
          
          ⁢
          
            
              1
              
                
                  r
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          
          ⁢
          
            [
            
              
                
                  A
                
                
                  A
                
                
                  ...
                
                
                  C
                
              
              
                
                  
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      -
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                    
                    ⁢
                    A
                  
                
                
                  ...
                
                
                  
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    C
                  
                
              
            
            ]
          
        
      
    
  




  or




  
    
      
        
          W
          =
          
          ⁢
          
            
              1
              
                r
              
            
            ⁡
            
              [
              
                
                  
                    
                      W
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      W
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      
                        
                          ...
                        
                        
                          
                            W
                            
                              (
                              r
                              )
                            
                          
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          =
          
          ⁢
          
            
              1
              
                
                  r
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      
                        
                          2
                          -
                          
                            
                              
                              α
                              
                            
                            2
                          
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      
                    
                  
                  
                    
                      α
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          
                            n
                            t
                          
                          /
                          2
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        
          
          ⁢
          
            [
            
              
                
                  A
                
                
                  A
                
                
                  ...
                
                
                  C
                
              
              
                
                  
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                    ⁢
                    A
                  
                
                
                  
                    
                      -
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                    
                    ⁢
                    A
                  
                
                
                  ...
                
                
                  
                    
                      -
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          φ
                        
                      
                    
                    ⁢
                    C
                  
                
              
            
            ]
          
        
      
    
  



When r is an even number,




  
    
      
        W
        =
        
        ⁢
        
          
            1
            
              r
            
          
          ⁡
          
            [
            
              
                
                  
                    W
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      2
                      )
                    
                  
                
                
                  ...
                
                
                  
                    W
                    
                      (
                      
                        r
                        -
                        1
                      
                      )
                    
                  
                
                
                  
                    W
                    
                      (
                      r
                      )
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            1
            
              
                r
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    
                      
                        2
                        -
                        
                          
                            
                            α
                            
                          
                          2
                        
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        
                          n
                          t
                        
                        /
                        2
                      
                    
                  
                
              
            
            ]
          
        
      
    
  
  
    
      
        
        ⁢
        
          [
          
            
              
                A
              
              
                A
              
              
                ...
              
              
                C
              
              
                C
              
            
            
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  A
                
              
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
              
              
                ...
              
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                  ⁢
                  C
                
              
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                      ⁢
                      
                        
                      
                      ⁢
                      C
                    
                  
                
              
            
          
          ]
        
      
    
  




In this example, A, B, . . . , C may be orthogonal to each other.
Observation
The following collusion may be made. That is, the minimum requirement for achieving the excellent performance of a recommended precoding matrix may follow as:

W=W2W1 

Here, an outer matrix W1 corresponds to a unitary precoding matrix that is an element of a first codebook C1 and has a dimension of Nt×R. For each rank, W1 may be expressed as follows:



  
    
      Rank
      ⁢
      
        
      
      ⁢
      1
      ⁢
      
        :
      
      ⁢
      
        
      
      ⁢
      
        W
        1
      
    
    =
    
      
        
          2
        
        2
      
      ⁡
      
        [
        
          
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  




  
    
      Rank
      ⁢
      
        
      
      ⁢
      2
      ⁢
      
        :
      
      ⁢
      
        
      
      ⁢
      
        W
        1
      
    
    =
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  



Rank r:

    
    
        when r is an odd number:
    
    





  
    
      W
      1
    
    =
    
      
        1
        
          
            
              r
              ⁢
              
                
              
            
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
            
              ...
            
            
              C
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  
                    -
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        φ
                      
                    
                  
                  ⁢
                  A
                
                ⁢
                
                  
                
              
            
            
              ...
            
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                C
              
            
          
        
        ]
      
    
  




  or




  
    
      W
      1
    
    =
    
      
        1
        
          
            r
          
          ⁢
          
            
              2
              ⁢
              
                
              
            
          
        
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
            
              ...
            
            
              C
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
            
              ...
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                C
              
            
          
        
        ]
      
    
  



    
    
        when r is an even number:
    
    






  
    W
    1
  
  =
  
    
      1
      
        
          r
        
        ⁢
        
          2
        
      
    
    ⁡
    
      [
      
        
          
            A
          
          
            A
          
          
            ...
          
          
            C
          
          
            C
          
        
        
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              A
            
          
          
            
              
                -
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
              
              ⁢
              A
            
          
          
            ...
          
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              C
            
          
          
            
              
                -
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
              
              ⁢
              C
            
          
        
      
      ]
    
  




A, B, . . . , C may be orthogonal to each other, or may be DFT vectors.
An inner matrix W2 may correspond to a diagonal matrix that is an element of a second codebook C2 and has a dimension of Nt×Nt. For example,




  
    W
    2
  
  =
  
    
      
        [
        
          
            
              
                
                  
                    2
                    -
                    
                      
                        
                        α
                        
                      
                      2
                    
                  
                
                ⁢
                
                  I
                  
                    
                      n
                      t
                    
                    /
                    2
                  
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                α
                ⁢
                
                  
                
                ⁢
                
                  I
                  
                    
                      n
                      t
                    
                    /
                    2
                  
                
              
            
          
        
        ]
      
      ⁢
      
        
      
      ⁢
      with
      ⁢
      
        
      
      ⁢
      
        
        α
        
      
    
    =
    1.
  




Extension
In the aforementioned observation, highly correlated channels may be assumed. Feedback overhead required for reporting W2 and W1 with a sufficient accuracy may not be used. To provide some design flexibilities, and to provide balanced feedback overheard and high feedback accuracy with respect to W2 and W1, a previous observation may be extended as follows:

W=W2W1 

In this example, an outer matrix W1 corresponds to a unitary precoding matrix that is an element of a first codebook C1 and has a dimension of Nt×R. For each rank, W1 may be expressed as follows:



  
    
      Rank
      ⁢
      
        
      
      ⁢
      1
      ⁢
      
        :
      
      ⁢
      
        
      
      ⁢
      
        W
        1
      
    
    =
    
      
        
          2
        
        2
      
      ⁡
      
        [
        
          
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  




  
    
      Rank
      ⁢
      
        
      
      ⁢
      2
      ⁢
      
        :
      
      ⁢
      
        
      
      ⁢
      
        W
        1
      
    
    =
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
  



Rank r:

    
    
        when r is an odd number:
    
    





  
    
      W
      1
    
    =
    
      
        1
        
          
            r
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
            
              ...
            
            
              C
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
            
              ...
            
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                C
              
            
          
        
        ]
      
    
  




  or




  
    
      W
      1
    
    =
    
      
        1
        
          
            r
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
            
              ...
            
            
              C
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
            
              ...
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                C
              
            
          
        
        ]
      
    
  



    
    
        when r is an even number:
    
    






  
    W
    1
  
  =
  
    
      1
      
        
          r
        
        ⁢
        
          2
        
      
    
    ⁡
    
      [
      
        
          
            A
          
          
            A
          
          
            ...
          
          
            C
          
          
            C
          
        
        
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              A
            
          
          
            
              
                -
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
              
              ⁢
              A
            
          
          
            ...
          
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
              ⁢
              C
            
          
          
            
              
                -
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
              
              ⁢
              C
            
          
        
      
      ]
    
  




A, B, . . . , C may be orthogonal to each other, or may be DFT vectors.
An inner matrix W2 may correspond to a diagonal matrix that is an element of a second codebook C2 and has a dimension of Nt×Nt. For example,




  
    W
    2
  
  =
  
    
      
        [
        
          
            
              
                
                  
                    2
                    -
                    
                      
                        
                        α
                        
                      
                      2
                    
                  
                
                ⁢
                Θ
              
            
            
              
                0
                
                  4
                  ×
                  4
                
              
            
          
          
            
              
                0
                
                  4
                  ×
                  4
                
              
            
            
              
                α
                ⁢
                
                  
                
                ⁢
                Θ
              
            
          
        
        ]
      
      ⁢
      
        
      
      ⁢
      with
      ⁢
      
        
      
      ⁢
      
        
        α
        
      
    
    =
    1.
  




In W2, Θ corresponds to a 4×4 matrix, and may be defined as Θ=diag{1,ejπθ,ej2πθ,ej3πθ}. diag(a, b, c, d) corresponds to a diagonal matrix that includes a, b, c, and d as diagonal elements. Θ enables tracking of a spatial correlation structure, for example, a DFT structure in a subband level above antennas 0 through 3, and above antennas 4 through 7. In this example, in a dual polarization case, the antennas 0 through 3 may generate one polarization, and the antennas 4 through 7 may generate another polarization. In a single polarization case, all the antennas may generate the same polarization.
α corresponds to a complex scalar and may process dual polarization or single polarization based on a small antennal interval. α may be selected within a subband level, for example, within a set of 1, j, ej4πθ. For example, in a single polarization case, W2 may have a structure of W2=diag{1,ejπθ,ej2πθ,ej3πθ,ej4πθ,ej5πθ,ej6πθ,ej7πθ}. In a dual polarization case, α may be selected as 1 or j.
Codebook Suggestions
Prior to suggesting codebooks, 4×r DFT matrices may be defined as follows:




  
    
      DFT
      1
    
    =
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              1
            
            
              1
            
            
              1
            
            
              1
            
          
          
            
              1
            
            
              j
            
            
              
                -
                1
              
            
            
              
                -
                j
              
            
          
          
            
              1
            
            
              
                -
                1
              
            
            
              1
            
            
              
                -
                1
              
            
          
          
            
              1
            
            
              
                -
                j
              
            
            
              
                -
                1
              
            
            
              j
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    
      DFT
      2
    
    =
    
      diag
      ⁢
      
        {
        
          1
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                π
                /
                4
              
            
          
          ,
          j
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              3
              ⁢
              
                π
                /
                4
              
            
          
        
        }
      
      ⁢
      
        DFT
        1
      
    
  
  ,
  
    

  
  ⁢
  
    
      DFT
      3
    
    =
    
      diag
      ⁢
      
        {
        
          1
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                π
                ⁢
                
                  
                
                /
                8
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              2
              ⁢
              
                π
                ⁢
                
                  
                
                /
                8
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              3
              ⁢
              
                π
                ⁢
                
                  
                
                /
                8
              
            
          
        
        }
      
      ⁢
      
        DFT
        1
      
    
  
  ,
  
    

  
  ⁢
  
    
      DFT
      4
    
    =
    
      diag
      ⁢
      
        {
        
          1
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              3
              ⁢
              
                π
                ⁢
                
                  
                
                /
                8
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              6
              ⁢
              
                π
                ⁢
                
                  
                
                /
                8
              
            
          
          ,
          
            e
            
              j9π
              /
              8
            
          
        
        }
      
      ⁢
      
        DFT
        1
      
    
  
  ,




Suggestion 1: 4-Bit Codebook for Each Rank for W1 
In suggestion 1, the first codebook C1 for rank r where r=1, . . . , 6 may include 16 4-bit elements or codewords. The first codebook C1 for rank r where r=7, 8 may include four elements.
Codebook C1 
The first codebook C1 for rank r may be expressed as C1,r.
A first codebook C1,1 for rank 1 may be obtained by employing columns 1 through 16 of the following matrix:




  
    V
    1
  
  =
  
    
      
        2
      
      2
    
    ⁡
    
      [
      
        
          
            
              DFT
              1
            
          
          
            
              DFT
              2
            
          
          
            
              DFT
              3
            
          
          
            
              DFT
              4
            
          
        
        
          
            
              DFT
              1
            
          
          
            
              -
              
                DFT
                2
              
            
          
          
            
              j
              ⁢
              
                
              
              ⁢
              
                DFT
                3
              
            
          
          
            
              
                -
                j
              
              ⁢
              
                
              
              ⁢
              
                DFT
                4
              
            
          
        
      
      ]
    
  




The 16 column vectors may correspond to DFT vectors for eight transmit antennas.
A first codebook C1,2 for rank 2 may include the following 16 matrices:




  
    C
    
      1
      ,
      2
    
  
  =
  
    {
    
      
        
          
            
              
                
                  
                    
                      1
                      2
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              D
                              
                                1
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                1
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              D
                              
                                1
                                ,
                                k
                              
                            
                          
                          
                            
                              -
                              
                                D
                                
                                  1
                                  ,
                                  k
                                
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ,
                  
                    
                      1
                      2
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              D
                              
                                2
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                2
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              D
                              
                                2
                                ,
                                k
                              
                            
                          
                          
                            
                              -
                              
                                D
                                
                                  2
                                  ,
                                  k
                                
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ,
                
              
            
            
              
                
                  
                    
                      1
                      2
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              D
                              
                                3
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                3
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              j
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  3
                                  ,
                                  k
                                
                              
                            
                          
                          
                            
                              
                                -
                                j
                              
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  3
                                  ,
                                  k
                                
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ,
                  
                    
                      1
                      2
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              D
                              
                                4
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                4
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              j
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  4
                                  ,
                                  k
                                
                              
                            
                          
                          
                            
                              
                                -
                                j
                              
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  4
                                  ,
                                  k
                                
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ,
                
              
            
          
        
      
      
        
          
            
              k
              =
              1
            
            ,
            ...
            ⁢
            
              
            
            ,
            4
          
        
      
    
    }
  




In this example, Dm,k corresponds to a kth column of DFTm. For example, D1,k corresponds to a kth column of DFT1, D2,k corresponds to a kth column of DFT2, D3,k corresponds to a kth column of DFT3, and D4,k corresponds to a kth column of DFT4.
The first codebook C1,2 may be obtained by using a first codebook for rank 1 and by adding up orthogonal columns based on




  
    W
    1
  
  =
  
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
          
          
            
              
                
                  e
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    φ
                  
                
                ⁢
                A
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
    .
  




A first codebook C1,3 for rank 3 may include the following 16 matrices:
Example 1)




  
    C
    
      1
      ,
      3
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          
                            1
                            ,
                            k
                          
                          ⁢
                          
                            
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          
                            2
                            ,
                            k
                          
                          ⁢
                          
                            
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    }
  




In this example, k=1, . . . 4 and m=k mod 4+1.
Example 2)




  
    C
    
      1
      ,
      3
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            
                              2
                              ,
                              m
                            
                            ⁢
                            
                              
                            
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                
                  
                    
                      1
                      
                        
                          3
                        
                        ⁢
                        
                          2
                        
                      
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              D
                              
                                3
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                3
                                ,
                                k
                              
                            
                          
                          
                            
                              D
                              
                                3
                                ,
                                m
                              
                            
                          
                        
                        
                          
                            
                              j
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  3
                                  ,
                                  k
                                
                              
                            
                          
                          
                            
                              
                                -
                                j
                              
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  3
                                  ,
                                  k
                                
                              
                            
                          
                          
                            
                              
                                -
                                j
                              
                              ⁢
                              
                                
                              
                              ⁢
                              
                                D
                                
                                  3
                                  ,
                                  m
                                
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ,
                
              
            
            
              
                
                  
                    1
                    
                      
                        3
                      
                      ⁢
                      
                        2
                      
                    
                  
                  ⁡
                  
                    [
                    
                      
                        
                          
                            D
                            
                              4
                              ,
                              k
                            
                          
                        
                        
                          
                            D
                            
                              4
                              ,
                              k
                            
                          
                        
                        
                          
                            D
                            
                              4
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          
                            j
                            ⁢
                            
                              
                            
                            ⁢
                            
                              D
                              
                                4
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              -
                              j
                            
                            ⁢
                            
                              
                            
                            ⁢
                            
                              D
                              
                                4
                                ,
                                k
                              
                            
                          
                        
                        
                          
                            
                              -
                              j
                            
                            ⁢
                            
                              
                            
                            ⁢
                            
                              D
                              
                                4
                                ,
                                m
                              
                            
                          
                        
                      
                    
                    ]
                  
                
              
            
          
        
      
    
    }
  




In this example, k=1, . . . 4 and m=k mod 4+1.
Other examples may also be used. For example, m may be given to be different from above, and k may also be given to be different from above. For example, various combinations of k and m may be given as (k,m)={(1,2),(1,3),(1,4),(2,3)}.
A first codebook C1,4 for rank 4 may include the following 16 matrices:
Example 1)




  
    C
    
      1
      ,
      4
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    }
  




In this example, k=1, . . . 4 and m=k mod 4+1.
Example 2) m may be given to be different from above, and k may also be given to be different from above. For example, various combinations of k and m may be given as (k,m)={(1,2),(1,3),(1,4),(2,3)}. Other examples may also be used.
A first codebook C1,5 for rank 5 may include the following 16 matrices:
Example 1)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  5
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




A combination of k,m, and n may be selected from {(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
Example 2)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  5
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




A combination of k,m, and n may be selected from {(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
A first codebook C1,6 for rank 6 may include the following 16 matrices:




  
    C
    
      1
      ,
      6
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  6
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




A combination of k,m, and n may be selected from {(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
A first codebook C1,7 for rank 7 may include the following four matrices:
Example 1)



  
    
      C
      
        1
        ,
        7
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            p
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            p
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              p
                            
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    
      (
      
        k
        ,
        m
        ,
        n
        ,
        p
      
      )
    
    =
    
      
        (
        
          1
          ,
          2
          ,
          3
          ,
          4
        
        )
      
      .
    
  



Example 2)



  
    
      C
      
        1
        ,
        7
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              1
                              ,
                              p
                            
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          -
                          
                            D
                            
                              2
                              ,
                              p
                            
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                
                  1
                  
                    
                      7
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                      
                        
                          D
                          
                            3
                            ,
                            p
                          
                        
                      
                    
                    
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              k
                            
                          
                        
                      
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              m
                            
                          
                        
                      
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              n
                            
                          
                        
                      
                      
                        
                          
                            -
                            j
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              3
                              ,
                              p
                            
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
        
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    
      (
      
        k
        ,
        m
        ,
        n
        ,
        p
      
      )
    
    =
    
      
        (
        
          1
          ,
          2
          ,
          3
          ,
          4
        
        )
      
      .
    
  



A first codebook C1,8 for rank 8 may include the following four matrices:




  
    C
    
      1
      ,
      8
    
  
  =
  
    {
    
      
        
          1
          
            
              8
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  D
                  1
                
              
              
                
                  D
                  1
                
              
            
            
              
                
                  D
                  1
                
              
              
                
                  -
                  
                    D
                    1
                  
                
              
            
          
          ]
        
      
      ,
      
        
          1
          
            
              8
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  D
                  2
                
              
              
                
                  D
                  2
                
              
            
            
              
                
                  D
                  2
                
              
              
                
                  -
                  
                    D
                    2
                  
                
              
            
          
          ]
        
      
      ,
      
        
          1
          
            
              8
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  D
                  3
                
              
              
                
                  D
                  3
                
              
            
            
              
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    D
                    3
                  
                
              
              
                
                  
                    -
                    j
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    D
                    3
                  
                
              
            
          
          ]
        
      
      ,
      
        
          1
          
            
              8
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  D
                  4
                
              
              
                
                  D
                  4
                
              
            
            
              
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    D
                    4
                  
                
              
              
                
                  
                    -
                    j
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    D
                    4
                  
                
              
            
          
          ]
        
      
    
    }
  




Codebook C2 
A number of codewords to be assigned to Θ and α may need to be carefully investigated.
Example 1) For example, when a single bit is assigned to Θ and α, the second codebook C2 may be expressed as follows:

    
    
        For rank 2:
    
    


With respect to α ε {ej4πθi} and Θi where i=1,2, when a second codebook for rank 1 including a first codeword and a second codeword is assumed as C2,1 . . . 2,




  
    C
    
      2
      ,
      
        1
        ⁢
        
          
        
        ⁢
        ...
        ⁢
        
          
        
        ⁢
        2
      
    
  
  =
  
    
      {
      
        
          [
          
            
              
                
                  Θ
                  1
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      4
                      ⁢
                      
                        πθ
                        1
                      
                    
                  
                  ⁢
                  
                    Θ
                    1
                  
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  Θ
                  2
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      4
                      ⁢
                      
                        πθ
                        2
                      
                    
                  
                  ⁢
                  
                    Θ
                    2
                  
                
              
            
          
          ]
        
      
      }
    
    .
  




In this example,




  
    
      θ
      1
    
    =
    
      1
      16
    
  
  ,
  
    
      θ
      2
    
    =
    
      
        
          -
          1
        
        16
      
      .
    
  




With respect to α ε {1,−1} and Θ=I, when the second codebook for rank 1 including a third codeword and a fourth codeword is assumed as C2,3 . . . 4,




  
    C
    
      2
      ,
      
        3
        ⁢
        
          
        
        ⁢
        ...
        ⁢
        
          
        
        ⁢
        4
      
    
  
  =
  
    
      {
      
        
          [
          
            
              
                
                  I
                  4
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  I
                  4
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  I
                  4
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  -
                  
                    I
                    4
                  
                
              
            
          
          ]
        
      
      }
    
    .
  




    
    
        For ranks 2, 3, and 4:
    
    


With respect to α ε {1} and Θi where i=1, 2, when a second codebook for ranks 2, 3, and 4 including a first codeword and a second codeword is assumed as C2,1 . . . 2,




  
    C
    
      2
      ,
      
        1
        ⁢
        
          
        
        ⁢
        ...
        ⁢
        
          
        
        ⁢
        2
      
    
  
  =
  
    
      {
      
        
          [
          
            
              
                
                  Θ
                  1
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  Θ
                  1
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  Θ
                  2
                
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  Θ
                  2
                
              
            
          
          ]
        
      
      }
    
    .
  




Example 2) A size of the second codebook may be extended to three bits by extending the aforementioned example 1).

    
    
        For rank 1:
    
    


With respect to α ε {1,ej4πθi} and Θi where i=1,2, when the second codebook for rank 1 including four codewords is assumed as




  
    
  
  ⁢
  
    
      C
      
        2
        ,
        
          1
          ⁢
          
            
          
          ⁢
          ...
          ⁢
          
            
          
          ⁢
          4
        
      
    
    ,
    
      

    
    ⁢
    
      
        C
        
          2
          ,
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            4
          
        
      
      =
      
        
          {
          
            
              [
              
                
                  
                    
                      Θ
                      1
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          4
                          ⁢
                          
                            πθ
                            1
                          
                        
                      
                      ⁢
                      
                        Θ
                        1
                      
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      2
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      
                        e
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          4
                          ⁢
                          
                            πθ
                            2
                          
                        
                      
                      ⁢
                      
                        Θ
                        2
                      
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      1
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      1
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      2
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      2
                    
                  
                
              
              ]
            
          
          }
        
        .
      
    
  




    
    
        For ranks 2, 3, and 4:
    
    


With respect to α ε {1} and Θi where i=1,2, when the second codebook for ranks 2, 3, and 4 including first through fourth codewords is assumed as




  
    
  
  ⁢
  
    
      C
      
        2
        ,
        
          1
          ⁢
          
            
          
          ⁢
          ...
          ⁢
          
            
          
          ⁢
          4
        
      
    
    ,
    
      

    
    ⁢
    
      
        C
        
          2
          ,
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            4
          
        
      
      =
      
        
          {
          
            
              [
              
                
                  
                    
                      Θ
                      1
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      1
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      2
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      2
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      3
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      3
                    
                  
                
              
              ]
            
            ,
            
              [
              
                
                  
                    
                      Θ
                      4
                    
                  
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                
                
                  
                    
                      0
                      
                        4
                        ×
                        4
                      
                    
                  
                  
                    
                      Θ
                      4
                    
                  
                
              
              ]
            
          
          }
        
        .
      
    
  




In this example,




  
    
      θ
      1
    
    =
    
      1
      16
    
  
  ,
  
    
      θ
      2
    
    =
    
      
        -
        1
      
      16
    
  
  ,
  
    
      θ
      3
    
    ⁢
    
      1
      8
    
  
  ,
  
    
      θ
      4
    
    =
    
      
        
          -
          1
        
        8
      
      .
    
  




With respect to α ε {1,j} and Θ=I, when the second codebook for ranks 2, 3, and 4 including fifth through sixth codewords is assumed as C2,5 . . . 6,




  
    C
    
      2
      ,
      
        5
        ⁢
        
          
        
        ⁢
        ...
        ⁢
        
          
        
        ⁢
        6
      
    
  
  =
  
    
      {
      
        
          [
          
            
              
                I
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                I
              
            
          
          ]
        
        ,
        
          [
          
            
              
                I
              
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
            
            
              
                
                  0
                  
                    4
                    ×
                    4
                  
                
              
              
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  I
                
              
            
          
          ]
        
      
      }
    
    .
  




With respect to




  
    
      θ
      3
    
    =
    
      1
      8
    
  
  ,
  
    
      θ
      4
    
    =
    
      
        -
        1
      
      8
    
  




with α ε {j}, when the second codebook for ranks 2, 3, and 4 including seventh through eighth codewords is assumed as





  
    C
    
      2
      ,
      
        7
        ⁢
        
          
        
        ⁢
        ...
        ⁢
        
          
        
        ⁢
        8
      
    
  
  ,
  
    
      C
      
        2
        ,
        
          7
          ⁢
          
            
          
          ⁢
          ...
          ⁢
          
            
          
          ⁢
          8
        
      
    
    =
    
      
        {
        
          
            [
            
              
                
                  
                    Θ
                    3
                  
                
                
                  
                    0
                    
                      4
                      ×
                      4
                    
                  
                
              
              
                
                  
                    0
                    
                      4
                      ×
                      4
                    
                  
                
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Θ
                      3
                    
                  
                
              
            
            ]
          
          ,
          
            [
            
              
                
                  
                    Θ
                    4
                  
                
                
                  
                    0
                    
                      4
                      ×
                      4
                    
                  
                
              
              
                
                  
                    0
                    
                      4
                      ×
                      4
                    
                  
                
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Θ
                      4
                    
                  
                
              
            
            ]
          
        
        }
      
      .
    
  




Suggestion 2: Maximum 4-Bit Codebook for Each Rank for W1 
In suggestion 2, the first codebook for rank r where r=1, . . . 2 may include 16 elements, the first codebook for rank r where r=3, 4 may include eight elements, and the first codebook for rank r where r=5, 6, 7, 8 may include four elements.
The above 64 entries may be divided into four subsets each including 16 entries. To indicate one of the subsets, two bits may be used. The two bits may indicate a rank corresponding to the selected subset among rank 1, rank 2, rank 3-4, and rank 5-8.
Codebook C1 
A first codebook C1 for rank r may be indicated as C1,r.
A rank 1 first codebook C1,1 may be obtained by employing columns 1 through 16 of the following matrix:




  
    V
    1
  
  =
  
    
      
        2
      
      2
    
    ⁡
    
      [
      
        
          
            
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                1
              
            
          
          
            
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                2
              
            
          
          
            
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                3
              
            
          
          
            
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                4
              
            
          
        
        
          
            
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                1
              
            
          
          
            
              
                -
                D
              
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                2
              
            
          
          
            
              j
              ⁢
              
                
              
              ⁢
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                3
              
            
          
          
            
              
                -
                j
              
              ⁢
              
                
              
              ⁢
              D
              ⁢
              
                
              
              ⁢
              F
              ⁢
              
                
              
              ⁢
              
                T
                4
              
            
          
        
      
      ]
    
  




The column vectors 1 through 16 may correspond to DFT vectors for eight transmit antennas.
A rank 2 first codebook C1,2 may include the following 16 matrices:




  
    C
    
      1
      ,
      2
    
  
  =
  
    {
    
      
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            4
                            ,
                            k
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              k
              =
              1
            
            ,
            ...
            ⁢
            
              
            
            ,
            4
          
        
      
    
    }
  




In this example, Dm,k corresponds to a kth column of DFTm. For example, D1,k corresponds to a kth column of DFT1, D2,k corresponds to a kth column of DFT2, D3,k corresponds to a kth column of DFT3, and D4,k corresponds to a kth column of DFT4.
The rank 2 first codebook C1,2 may be obtained by using the rank 1 first codebook and adding orthogonal columns based on




  
    W
    1
  
  =
  
    
      
        1
        2
      
      ⁡
      
        [
        
          
            
              A
            
            
              A
            
          
          
            
              
                e
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  φ
                
              
            
            
              
                
                  -
                  
                    e
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      φ
                    
                  
                
                ⁢
                A
              
            
          
        
        ]
      
    
    .
  




A rank 3 first codebook C1,3 may include the following eight matrices:
Example 1)




  
    C
    
      1
      ,
      3
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  3
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, k=1, 2 and m=k+2.
Example 2)




  
    C
    
      1
      ,
      3
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  3
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, k=1, 2 and m=k+2.
Example 3)



  
    
      C
      
        1
        ,
        3
      
    
    =
    
      {
      
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      C
      
        1
        ,
        3
      
    
    =
    
      {
      
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        m
                      
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                
              
            
            ]
          
        
      
      }
    
  



In this example, k=1, . . . , 4 and m=k mod 4+1.
Example 4)



  
    
      C
      
        1
        ,
        3
      
    
    =
    
      {
      
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      C
      
        1
        ,
        3
      
    
    =
    
      {
      
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      1
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      1
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        1
                        ,
                        m
                      
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    D
                    
                      2
                      ,
                      m
                    
                  
                
              
              
                
                  
                    D
                    
                      2
                      ,
                      k
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                
                
                  
                    -
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                
              
            
            ]
          
        
      
      }
    
  



In this example, (k,m)={(1,2),(1,3),(1,4),(2,3)}.
In addition to examples 1) through 4), other examples may also be employed.
A rank 4 first codebook C1,4 may include the following eight matrices:
Example 1)




  
    C
    
      1
      ,
      4
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  4
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, k=1, 2 and m=k+2.
Example 2)




  
    C
    
      1
      ,
      4
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  4
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m)={(1,2),(1,3)}.
Example 3)




  
    C
    
      1
      ,
      4
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
    
    }
  




In this example, (k,m)={(1,2),(1,3),(1,4),(2,3)}.
In addition to examples 1) through 4), other examples may also be employed.
The rank 5 first codebook C1,5 may include the following four matrices:
Example 1)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        1
        
          
            5
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
          
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    k
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    m
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
          
        
        ]
      
    
    }
  




In this example, (k,m,n)={(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
Example 2)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        1
        
          
            5
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
          
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    k
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    m
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
          
        
        ]
      
    
    }
  




In this example, (k,m,n)={(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
Example 3)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        
          
            
              1
              
                
                  5
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      D
                      
                        1
                        ,
                        k
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        m
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      D
                      
                        1
                        ,
                        n
                      
                    
                  
                
              
              ]
            
          
        
      
      
        
          
            
              1
              
                
                  5
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        n
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n)={(1,2,3),(1,2,4)}.
Example 4)




  
    C
    
      1
      ,
      5
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    5
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  5
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n)={(1,2,3)}.
A rank 6 first codebook C1,6 may include the following four matrices:
Example 1)




  
    C
    
      1
      ,
      6
    
  
  =
  
    {
    
      
        1
        
          
            6
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
          
          
            
              
                D
                
                  1
                  ,
                  k
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    k
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  m
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    m
                  
                
              
            
            
              
                D
                
                  1
                  ,
                  n
                
              
            
            
              
                -
                
                  D
                  
                    1
                    ,
                    n
                  
                
              
            
          
        
        ]
      
    
    }
  




In this example, (k,m,n)={(1,2,3),(1,2,4),(1,3,4),(2,3,4)}.
Example 2)




  
    C
    
      1
      ,
      6
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  6
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      D
                      
                        2
                        ,
                        k
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        m
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      D
                      
                        2
                        ,
                        n
                      
                    
                  
                  
                    
                      -
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n)={(1,2,3),(1,2,4)}.
Example 3)




  
    C
    
      1
      ,
      6
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    6
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  6
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n)={(1,2,3)}.
A rank 7 first codebook C1,7 may include the following four matrices:
Example 1)




  
    C
    
      1
      ,
      7
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          p
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          p
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  7
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        p
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          p
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n, p)={(1,2,3,4)}.
Example 2)




  
    C
    
      1
      ,
      7
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          1
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          1
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            1
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        D
                        
                          2
                          ,
                          k
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          m
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        D
                        
                          2
                          ,
                          n
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        -
                        
                          D
                          
                            2
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    7
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          k
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          m
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          n
                        
                      
                    
                    
                      
                        D
                        
                          3
                          ,
                          p
                        
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            k
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            m
                          
                        
                      
                    
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            n
                          
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          
                            3
                            ,
                            p
                          
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              1
              
                
                  7
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        k
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        m
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        n
                      
                    
                  
                  
                    
                      D
                      
                        4
                        ,
                        p
                      
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          k
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          m
                        
                      
                    
                  
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          n
                        
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          4
                          ,
                          p
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




In this example, (k,m,n,p)=(1,2,3,4).
A rank 8 first codebook C1,8 may include the following four matrices:




  
    C
    
      1
      ,
      8
    
  
  =
  
    {
    
      
        
          
            
              
                1
                
                  
                    8
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        1
                      
                    
                    
                      
                        D
                        1
                      
                    
                  
                  
                    
                      
                        D
                        1
                      
                    
                    
                      
                        -
                        
                          D
                          1
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
        
          
            
              
                1
                
                  
                    8
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        2
                      
                    
                    
                      
                        D
                        2
                      
                    
                  
                  
                    
                      
                        D
                        2
                      
                    
                    
                      
                        -
                        
                          D
                          2
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
      
      
        
          
            
              
                1
                
                  
                    8
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        D
                        3
                      
                    
                    
                      
                        D
                        3
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          3
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          D
                          3
                        
                      
                    
                  
                
                ]
              
            
            ,
          
        
        
          
            
              1
              
                
                  8
                
                ⁢
                
                  2
                
              
            
            ⁡
            
              [
              
                
                  
                    
                      D
                      4
                    
                  
                  
                    
                      D
                      4
                    
                  
                
                
                  
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        4
                      
                    
                  
                  
                    
                      
                        -
                        j
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        4
                      
                    
                  
                
              
              ]
            
          
        
      
    
    }
  




Codebook C2 
The second codebook C2 may be the same as in suggestion 1.
Suggestion 3: Maximum 4-Bit Codebook for Each Rank for W1 
Suggestion 3 relates to the structure of W1W2. In suggestion 3, the first codebook C1 for rank r where r=1, 2 may include 16 elements, the first codebook C1 for rank r where r=3, 4 may include eight elements, and the first codebook C1 for rank r where r=5, 6, 7, 8 may include four elements.
The above 64 entries may be divided into four subsets each including 16 entries. To indicate one of the subsets, two bits may be used. The two bits may indicate a rank corresponding to the selected subset among rank 1, rank 2, rank 3-4, and rank 5-8.
Codebook C1 
The first codebook C1 for rank r may be indicated as C1,r.
A first codebook C1,(1,2) for ranks 1 and 2 may be obtained by the following matrices:



  
    
      B
      =
      
        [
        
          
            
              
                b
                0
              
            
            
              
                b
                1
              
            
            
              ...
            
            
              
                b
                31
              
            
          
        
        ]
      
    
    ,
    
      

    
    ⁢
    
      
        
          [
          B
          ]
        
        
          
            1
            +
            m
          
          ,
          
            1
            +
            n
          
        
      
      =
      
        e
        
          j
          ⁢
          
            
              2
              ⁢
              π
              ⁢
              
                
              
              ⁢
              mn
            
            32
          
        
      
    
    ,
    
      

    
    ⁢
    
      m
      =
      0
    
    ,
    1
    ,
    2
    ,
    3
    ,
    
      n
      =
      0
    
    ,
    1
    ,
    
      ...
      ⁢
      
        
      
      ⁢
      31
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        b
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                          ⁢
                          
                            
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                
                                  
                                
                                ⁢
                                k
                              
                              +
                              1
                            
                            )
                          
                          ⁢
                          
                            
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                
                                  
                                
                                ⁢
                                k
                              
                              ⁢
                              
                                
                              
                              +
                              2
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                
                                  
                                
                                ⁢
                                k
                              
                              ⁢
                              
                                
                              
                              +
                              3
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                  
                
                ]
              
            
          
        
        
          
            
              
                
                  :
                  k
                
                =
                0
              
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              15
            
          
        
      
      }
    
  




  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              X
              
                (
                k
                )
              
            
          
        
      
      ]
    
  




  
    
      C
      
        1
        ,
        
          (
          
            1
            ,
            2
          
          )
        
      
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            15
            )
          
        
      
      }
    
  



In this example, [B]1+m,1+n indicates an element present in an (1+m)th row and an (1+n)th column among elements belonging to B, and bz(z=0, 1, 2, . . . , 31) corresponds to a zth column vector of the matrix B, and a mod b denotes a remainder when a is divided by b.
A first codebook C1,(3,4) for ranks 3 and 4 may be obtained by the following matrices:



  
    
      B
      =
      
        [
        
          
            
              
                b
                0
              
            
            
              
                b
                1
              
            
            
              ...
            
            
              
                b
                31
              
            
          
        
        ]
      
    
    ,
    
      

    
    ⁢
    
      
        
          [
          B
          ]
        
        
          
            1
            +
            m
          
          ,
          
            1
            +
            n
          
        
      
      =
      
        e
        
          j
          ⁢
          
            
              2
              ⁢
              π
              ⁢
              
                
              
              ⁢
              mn
            
            32
          
        
      
    
    ,
    
      

    
    ⁢
    
      m
      =
      0
    
    ,
    1
    ,
    2
    ,
    3
    ,
    
      n
      =
      0
    
    ,
    1
    ,
    
      ...
      ⁢
      
        
      
      ⁢
      31
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        b
                        
                          4
                          ⁢
                          
                            
                          
                          ⁢
                          k
                          ⁢
                          
                            
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                4
                                ⁢
                                
                                  
                                
                                ⁢
                                k
                              
                              +
                              1
                            
                            )
                          
                          ⁢
                          
                            
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      ...
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                4
                                ⁢
                                
                                  
                                
                                ⁢
                                k
                              
                              ⁢
                              
                                
                              
                              +
                              7
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                  
                
                ]
              
            
          
        
        
          
            
              
                
                  :
                  k
                
                =
                0
              
              ,
              1
              ,
              2
              ,
              3
              ,
              4
              ,
              5
              ,
              6
              ,
              7
            
          
        
      
      }
    
  




  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              X
              
                (
                k
                )
              
            
          
        
      
      ]
    
  




  
    
      C
      
        1
        ,
        
          (
          
            3
            ,
            4
          
          )
        
      
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            7
            )
          
        
      
      }
    
  



A first codebook C1,(5,6,7,8) for ranks 5, 6,7, and 8 may be obtained by the following matrices:



  
    
      
        X
        
          (
          0
          )
        
      
      =
      
        
          1
          2
        
        ×
        
          [
          
            
              
                1
              
              
                1
              
              
                1
              
              
                1
              
            
            
              
                1
              
              
                j
              
              
                
                  -
                  1
                
              
              
                
                  -
                  j
                
              
            
            
              
                1
              
              
                
                  -
                  1
                
              
              
                1
              
              
                
                  -
                  1
                
              
            
            
              
                1
              
              
                
                  -
                  j
                
              
              
                
                  -
                  1
                
              
              
                j
              
            
          
          ]
        
      
    
    ,
    
      

    
    ⁢
    
      
        X
        
          (
          1
          )
        
      
      =
      
        diag
        ⁢
        
          {
          
            1
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                
                  π
                  /
                  4
                
              
            
            ,
            j
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                3
                ⁢
                
                  π
                  /
                  4
                
              
            
          
          }
        
        ⁢
        
          X
          
            (
            0
            )
          
        
      
    
    ,
    
      

    
    ⁢
    
      
        X
        
          (
          2
          )
        
      
      =
      
        diag
        ⁢
        
          {
          
            1
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                
                  π
                  /
                  8
                
              
            
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                
                  π
                  /
                  8
                
              
            
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                3
                ⁢
                
                  π
                  /
                  8
                
              
            
          
          }
        
        ⁢
        
          X
          
            (
            0
            )
          
        
      
    
    ,
    
      

    
    ⁢
    
      
        X
        
          (
          3
          )
        
      
      =
      
        diag
        ⁢
        
          {
          
            1
            ,
            
              e
              
                j3π
                /
                8
              
            
            ,
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                6
                ⁢
                
                  π
                  /
                  8
                
              
            
            ,
            
              e
              
                j9π
                /
                8
              
            
          
          }
        
        ⁢
        
          X
          
            (
            0
            )
          
        
      
    
  




  
    
      
        W
        1
        
          (
          k
          )
        
      
      =
      
        {
        
          [
          
            
              
                
                  X
                  
                    (
                    k
                    )
                  
                
              
              
                0
              
            
            
              
                0
              
              
                
                  X
                  
                    (
                    k
                    )
                  
                
              
            
          
          ]
        
        }
      
    
    ,
    
      k
      =
      0
    
    ,
    1
    ,
    2
    ,
    3
  




  
    
      C
      
        1
        ,
        
          (
          
            5
            ,
            6
            ,
            7
            ,
            8
          
          )
        
      
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            3
            )
          
        
      
      }
    
  



Codebook C2 
The second codebook C2 for rank r may be indicated as C2,r.
A second codebook C2,1 for rank 1 may be expressed by:



  
    
      C
      
        2
        ,
        1
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    2
                  
                
                ⁡
                
                  [
                  
                    
                      
                        Y
                      
                    
                    
                      
                        Y
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                
                  1
                  
                    2
                  
                
                ⁡
                
                  [
                  
                    
                      
                        Y
                      
                    
                    
                      
                        
                          j
                          ⁢
                          
                            
                          
                          ⁢
                          Y
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                
                  1
                  
                    2
                  
                
                ⁡
                
                  [
                  
                    
                      
                        Y
                      
                    
                    
                      
                        
                          -
                          Y
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                1
                
                  2
                
              
              ⁡
              
                [
                
                  
                    
                      Y
                    
                  
                  
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        Y
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          
            e
            ~
          
          1
        
        ,
        
          
            e
            ~
          
          2
        
        ,
        
          
            e
            ~
          
          3
        
        ,
        
          
            e
            ~
          
          4
        
      
      }
    
  



A second codebook C2,2 for rank 2 may be expressed by:



  
    
      C
      
        2
        ,
        2
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    
                      2
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          Y
                          1
                        
                      
                      
                        
                          Y
                          2
                        
                      
                    
                    
                      
                        
                          Y
                          1
                        
                      
                      
                        
                          -
                          
                            Y
                            2
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                1
                
                  
                    2
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        Y
                        1
                      
                    
                    
                      
                        Y
                        2
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Y
                          1
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Y
                          2
                        
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          
            
              
                (
                
                  
                    
                      e
                      ~
                    
                    1
                  
                  ,
                  
                    
                      e
                      ~
                    
                    1
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    2
                  
                  ,
                  
                    
                      e
                      ~
                    
                    2
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    3
                  
                  ,
                  
                    
                      e
                      ~
                    
                    3
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    4
                  
                  ,
                  
                    
                      e
                      ~
                    
                    4
                  
                
                )
              
              ,
            
          
        
        
          
            
              
                (
                
                  
                    
                      e
                      ~
                    
                    1
                  
                  ,
                  
                    
                      e
                      ~
                    
                    2
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    2
                  
                  ,
                  
                    
                      e
                      ~
                    
                    3
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    1
                  
                  ,
                  
                    
                      e
                      ~
                    
                    4
                  
                
                )
              
              ,
              
                (
                
                  
                    
                      e
                      ~
                    
                    2
                  
                  ,
                  
                    
                      e
                      ~
                    
                    4
                  
                
                )
              
            
          
        
      
      }
    
  



In this example, {tilde over (e)}n corresponds to a selection vectors. An nth element of {tilde over (e)}n may have a value of 1 with respect to ranks 1 and 2 and all of remaining elements may have a value of zero.
A second codebook C2,3 for rank 3 may be expressed by



  
    
      C
      
        2
        ,
        3
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    
                      3
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        
                          Y
                          1
                        
                      
                      
                        
                          Y
                          2
                        
                      
                    
                    
                      
                        
                          Y
                          1
                        
                      
                      
                        
                          -
                          
                            Y
                            2
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                1
                
                  
                    3
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      
                        Y
                        1
                      
                    
                    
                      
                        Y
                        2
                      
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Y
                          1
                        
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Y
                          2
                        
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          
            
              
                (
                
                  
                    e
                    1
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            1
                          
                        
                        
                          
                            e
                            5
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    2
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            2
                          
                        
                        
                          
                            e
                            6
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
            
          
        
        
          
            
              
                (
                
                  
                    e
                    3
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            3
                          
                        
                        
                          
                            e
                            7
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    4
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            4
                          
                        
                        
                          
                            e
                            8
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
            
          
        
        
          
            
              
                (
                
                  
                    e
                    5
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            1
                          
                        
                        
                          
                            e
                            5
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    6
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            2
                          
                        
                        
                          
                            e
                            6
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
            
          
        
        
          
            
              
                (
                
                  
                    e
                    7
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            3
                          
                        
                        
                          
                            e
                            7
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    8
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            4
                          
                        
                        
                          
                            e
                            8
                          
                        
                      
                    
                    ]
                  
                
                )
              
            
          
        
      
      }
    
  



A second codebook C2,4 for rank 4 may be expressed by



  
    
      C
      
        2
        ,
        4
      
    
    =
    
      {
      
        
          
            
              
                
                  1
                  
                    
                      4
                    
                    ⁢
                    
                      2
                    
                  
                
                ⁡
                
                  [
                  
                    
                      
                        Y
                      
                      
                        Y
                      
                    
                    
                      
                        Y
                      
                      
                        
                          -
                          Y
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                1
                
                  
                    4
                  
                  ⁢
                  
                    2
                  
                
              
              ⁡
              
                [
                
                  
                    
                      Y
                    
                    
                      Y
                    
                  
                  
                    
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        Y
                      
                    
                    
                      
                        
                          -
                          j
                        
                        ⁢
                        
                          
                        
                        ⁢
                        Y
                      
                    
                  
                
                ]
              
            
          
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  1
                
              
              
                
                  e
                  5
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  3
                
              
              
                
                  e
                  7
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  



In this example, en corresponds to a 8×1 selection vectors. An nth element of en may have a value of 1 with respect to ranks 3 and 4, and all of remaining elements may have a value of zero.
A second codebook C2, (5,6,7,8) for ranks 5,6,7, and 8 may be obtained by the following matrices:



  
    
      C
      
        2
        ,
        5
      
    
    =
    
      
        1
        
          
            5
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                3
              
            
          
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  1
                
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  2
                
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  3
                
              
            
          
        
        ]
      
    
  




  
    
      C
      
        2
        ,
        6
      
    
    =
    
      
        1
        
          
            6
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                
                  e
                  ~
                
                3
              
            
          
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  1
                
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  2
                
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  3
                
              
            
          
        
        ]
      
    
  




  
    
      C
      
        2
        ,
        7
      
    
    =
    
      
        1
        
          
            7
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                
                  e
                  ~
                
                4
              
            
          
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  1
                
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  2
                
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  3
                
              
            
            
              
                
                  e
                  ~
                
                4
              
            
          
        
        ]
      
    
  




  
    
      C
      
        2
        ,
        8
      
    
    =
    
      
        1
        
          
            8
          
          ⁢
          
            2
          
        
      
      ⁡
      
        [
        
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                
                  e
                  ~
                
                4
              
            
            
              
                
                  e
                  ~
                
                4
              
            
          
          
            
              
                
                  e
                  ~
                
                1
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  1
                
              
            
            
              
                
                  e
                  ~
                
                2
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  2
                
              
            
            
              
                
                  e
                  ~
                
                3
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  3
                
              
            
            
              
                
                  e
                  ~
                
                4
              
            
            
              
                -
                
                  
                    e
                    ~
                  
                  4
                
              
            
          
        
        ]
      
    
  



In this example, {tilde over (e)}n corresponds to a 4×1 selection vectors. An nth element of {tilde over (e)}n may have a value of 1 with respect to ranks 5, 6, 7, and 8 and all of remaining elements may have a value of zero.
Hereinafter, digits of the first codebook C1 for W1 and the second codebook C2 for W2 will be described in detail. The overall codebook C for W that is defined by performing inner product between each of codewords of C1 and each of codewords of C2 will be described. That is, one of codewords belonging to the overall codebook C may be a precoding matrix W that is finally used by the transmitter.
Detailed Digits of First Codebook C1 
Hereinafter, ans(;,;,n) corresponds to an nth codeword in a first codebook corresponding to a corresponding transmission rank. Each of codewords may include a plurality of column vectors. For example, a first codeword ans(;,;,1) in the first codebook for ranks 1 and 2 may include eight column vectors.












Rank 1 and 2





ans(:, :, 1) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i







ans(:, :, 2) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 + 0.1913i
  0.4157 + 0.2778i
  0.3536 + 0.3536i
  0.2778 + 0.4157i



  0.3536 + 0.3536i
  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i



  0.1913 + 0.4619i
−0.0975 + 0.4904i
−0.3536 + 0.3536i
−0.4904 + 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
 0x







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 + 0.1913i
  0.4157 + 0.2778i
  0.3536 + 0.3536i
  0.2778 + 0.4157i



  0.3536 + 0.3536i
  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i



  0.3536 + 0.3536i
  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i







ans(:, :, 3) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i







ans(:, :, 4) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 + 0.4619i
  0.0975 + 0.4904i
  0.0000 + 0.5000i
−0.0975 + 0.4904i



−0.3536 + 0.3536i
−0.4619 + 0.1913i
−0.5000 + 0.0000i
−0.4619 − 0.1913i



−0.4619 − 0.1913i
−0.2778 − 0.4157i
−0.0000 − 0.5000i
  0.2778 − 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 + 0.4619i
  0.0975 + 0.4904i
  0.0000 + 0.5000i
−0.0975 + 0.4904i



−0.3536 + 0.3536i
−0.4619 + 0.1913i
−0.5000 + 0.0000i
−0.4619 − 0.1913i



−0.4619 − 0.1913i
−0.2778 − 0.4157i
−0.0000 − 0.5000i
  0.2778 − 0.4157i







ans(:, :, 5) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i







ans(:, :, 6) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.1913 + 0.4619i
−0.2778 + 0.4157i
−0.3536 + 0.3536i
−0.4157 + 0.2778i



−0.3536 − 0.3536i
−0.1913 − 0.4619i
−0.0000 − 0.5000i
  0.1913 − 0.4619i



  0.4619 − 0.1913i
  0.4904 + 0.0975i
  0.3536 + 0.3536i
  0.0975 + 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.1913 + 0.4619i
−0.2778 + 0.4157i
−0.3536 + 0.3536i
−0.4157 + 0.2778i



−0.3536 − 0.3536i
−0.1913 − 0.4619i
−0.0000 − 0.5000i
  0.1913 − 0.4619i



  0.4619 − 0.1913i
  0.4904 + 0.0975i
  0.3536 + 0.3536i
  0.0975 + 0.4904i







ans(:, :, 7) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i







ans(:, :, 8) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.4619 + 0.1913i
−0.4904 + 0.0975i
−0.5000 + 0.0000i
−0.4904 − 0.0975i



  0.3536 − 0.3536i
  0.4619 − 0.1913i
  0.5000 − 0.0000i
  0.4619 + 0.1913i



−0.1913 + 0.4619i
−0.4157 + 0.2778i
−0.5000 + 0.0000i
−0.4157 − 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.4619 + 0.1913i
−0.4904 + 0.0975i
−0.5000 + 0.0000i
−0.4904 − 0.0975i



  0.3536 − 0.3536i
  0.4619 − 0.1913i
  0.5000 − 0.0000i
  0.4619 + 0.1913i



−0.1913 + 0.4619i
−0.4157 + 0.2778i
−0.5000 + 0.0000i
−0.4157 − 0.2778i







ans(:, :, 9) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i



  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i



  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i







ans(:, :, 10) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.4619 − 0.1913i
−0.4157 − 0.2778i
−0.3536 − 0.3536i
−0.2778 − 0.4157i



  0.3536 + 0.3536i
  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i



−0.1913 − 0.4619i
  0.0975 − 0.4904i
  0.3536 − 0.3536i
  0.4904 − 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.4619 − 0.1913i
−0.4157 − 0.2778i
−0.3536 − 0.3536i
−0.2778 − 0.4157i



  0.3536 + 0.3536i
  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i



−0.1913 − 0.4619i
  0.0975 − 0.4904i
  0.3536 − 0.3536i
  0.4904 − 0.0975i







ans(:, :, 11) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i







ans(:, :, 12) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.1913 − 0.4619i
−0.0975 − 0.4904i
−0.0000 − 0.5000i
  0.0975 − 0.4904i



−0.3536 + 0.3536i
−0.4619 + 0.1913i
−0.5000 + 0.0000i
−0.4619 − 0.1913i



  0.4619 + 0.1913i
  0.2778 + 0.4157i
  0.0000 + 0.5000i
−0.2778 + 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.1913 − 0.4619i
−0.0975 − 0.4904i
−0.0000 − 0.5000i
  0.0975 − 0.4904i



−0.3536 + 0.3536i
−0.4619 + 0.1913i
−0.5000 + 0.0000i
−0.4619 − 0.1913i



  0.4619 + 0.1913i
  0.2778 + 0.4157i
  0.0000 + 0.5000i
−0.2778 + 0.4157i







ans(:, :, 13) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i







ans(:, :, 14) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 − 0.4619i
  0.2778 − 0.4157i
  0.3536 − 0.3536i
  0.4157 − 0.2778i



−0.3536 − 0.3536i
−0.1913 − 0.4619i
−0.0000 − 0.5000i
  0.1913 − 0.4619i



−0.4619 + 0.1913i
−0.4904 − 0.0975i
−0.3536 − 0.3536i
−0.0975 − 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 − 0.4619i
  0.2778 − 0.4157i
  0.3536 − 0.3536i
  0.4157 − 0.2778i



−0.3536 − 0.3536i
−0.1913 − 0.4619i
−0.0000 − 0.5000i
  0.1913 − 0.4619i



−0.4619 + 0.1913i
−0.4904 − 0.0975i
−0.3536 − 0.3536i
−0.0975 − 0.4904i







ans(:, :, 15) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i







ans(:, :, 16) =


columns 1-4












   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 − 0.1913i
  0.4904 − 0.0975i
   0.5000
  0.4904 + 0.0975i



  0.3536 − 0.3536i
  0.4619 − 0.1913i
   0.5000
  0.4619 + 0.1913i



  0.1913 − 0.4619i
  0.4157 − 0.2778i
   0.5000
  0.4157 + 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 − 0.1913i
  0.4904 − 0.0975i
   0.5000
  0.4904 + 0.0975i



  0.3536 − 0.3536i
  0.4619 − 0.1913i
   0.5000
  0.4619 + 0.1913i



  0.1913 − 0.4619i
  0.4157 − 0.2778i
   0.5000
  0.4157 + 0.2778i











Rank 3 and 4





ans(:, :, 1) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i







ans(:, :, 2) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i







ans(:, :, 3) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i







ans(:, :, 4) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i



  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i



  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i







ans(:, :, 5) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i



  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12









0
0
0


0
0
0


0
0
0


0
0
0


   0.5000
   0.5000
   0.5000


−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i


  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i


−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



   0.5000











−0.4157 − 0.2778i
−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i


  0.1913 + 0.4619i
  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i


  0.0975 − 0.4904i
  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i







ans(:, :, 6) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i



  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i



  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i







ans(:, :, 7) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i



−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i



  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i







ans(:, :, 8) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 9 through 12












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i



−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i



−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i







Columns 13 through 16












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i



   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i



   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i











Rank 5 and 6 and 7 and 8





ans(:, :, 1) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
    0 + 0.5000i
   −0.5000
    0 − 0.5000i



   0.5000
  −0.5000
   0.5000
   −0.5000



   0.5000
    0 − 0.5000i
   −0.5000
    0 + 0.5000i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



   0.5000
    0 + 0.5000i
   −0.5000
    0 − 0.5000i



   0.5000
   −0.5000
   0.5000
   −0.5000



   0.5000
    0 − 0.5000i
   −0.5000
    0 + 0.5000i







ans(:, :, 2) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
−0.3536 + 0.3536i
−0.3536 − 0.3536i
  0.3536 − 0.3536i



  0.0000 + 0.5000i
−0.0000 − 0.5000i
  0.0000 + 0.5000i
−0.0000 − 0.5000i



−0.3536 + 0.3536i
  0.3536 + 0.3536i
  0.3536 − 0.3536i
−0.3536 − 0.3536i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.3536 + 0.3536i
−0.3536 + 0.3536i
−0.3536 − 0.3536i
  0.3536 − 0.3536i



  0.0000 + 0.5000i
−0.0000 − 0.5000i
  0.0000 + 0.5000i
−0.0000 − 0.5000i



−0.3536 + 0.3536i
  0.3536 + 0.3536i
  0.3536 − 0.3536i
−0.3536 − 0.3536i







ans(:, :, 3) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 + 0.1913i
−0.1913 + 0.4619i
−0.4619 − 0.1913i
  0.1913 − 0.4619i



  0.3536 + 0.3536i
−0.3536 − 0.3536i
  0.3536 + 0.3536i
−0.3536 − 0.3536i



  0.1913 + 0.4619i
  0.4619 − 0.1913i
−0.1913 − 0.4619i
−0.4619 + 0.1913i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.4619 + 0.1913i
−0.1913 + 0.4619i
−0.4619 − 0.1913i
  0.1913 − 0.4619i



  0.3536 + 0.3536i
−0.3536 − 0.3536i
  0.3536 + 0.3536i
−0.3536 − 0.3536i



  0.1913 + 0.4619i
  0.4619 − 0.1913i
−0.1913 − 0.4619i
−0.4619 + 0.1913i







ans(:, :, 4) =


Columns 1 through 4












   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 + 0.4619i
−0.4619 + 0.1913i
−0.1913 − 0.4619i
  0.4619 − 0.1913i



−0.3536 + 0.3536i
  0.3536 − 0.3536i
−0.3536 + 0.3536i
  0.3536 − 0.3536i



−0.4619 − 0.1913i
−0.1913 + 0.4619i
  0.4619 + 0.1913i
  0.1913 − 0.4619i



0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0







Columns 5 through 8












0
0
0
0



0
0
0
0



0
0
0
0



0
0
0
0



   0.5000
   0.5000
   0.5000
   0.5000



  0.1913 + 0.4619i
−0.4619 + 0.1913i
−0.1913 − 0.4619i
  0.4619 − 0.1913i



−0.3536 + 0.3536i
  0.3536 − 0.3536i
−0.3536 + 0.3536i
  0.3536 − 0.3536i



−0.4619 − 0.1913i
−0.1913 + 0.4619i
  0.4619 + 0.1913i
  0.1913 − 0.4619i










Detailed Digits of Second Codebook C2 
Hereinafter, digits of codewords belonging to the second codebook C2 for a variety of ranks will be described in detail. (;,;,n) corresponds to an nth codeword in a second codebook corresponding to a corresponding transmission rank. Each of codewords may include at least one column vector.












- Rank 1





(:, :, 1) =







0.7071


0


0


0


0.7071


0


0


0







(:, :, 2) =







0.7071


0


0


0


0 + 0.7071i


0


0


0







(:, :, 3) =







0.7071


0


0


0


−0.7071


0


0


0







(:, :, 4) =







0.7071


0


0


0


0 − 0.7071i


0


0


0







(:, :, 5) =







0


0.7071


0


0


0


0.7071


0


0







(:, :, 6) =







0


0.7071


0


0


0


0 + 0.7071i


0


0







(:, :, 7) =







0


0.7071


0


0


0


−0.7071


0


0







(:, :, 8) =







0


0.7071


0


0


0


0 − 0.7071i


0


0







(:, :, 9) =







0


0


0.7071


0


0


0


0.7071


0







(:, :, 10) =







0


0


0.7071


0


0


0


0 + 0.7071i


0







(:, :, 11) =







0


0


0.7071


0


0


0


−0.7071


0







(:, :, 12) =







0


0


0.7071


0


0


0


0 − 0.7071i


0







(:, :, 13) =







0


0


0


0.7071


0


0


0


0.7071







(:, :, 14) =







0


0


0


0.7071


0


0


0


0 + 0.7071i







(:, :, 15) =







0


0


0


0.7071


0


0


0


−0.7071







(:, :, 16) =







0


0


0


0.7071


0


0


0


0 − 0.7071i










- Rank 2





(:, :, 1) =










   0.5000
0.5000



0
0



0
0



0
0



   0.5000
−0.5000



0
0



0
0



0
0







(:, :, 2) =










   0.5000
0.5000



0
0



0
0



0
0



0 + 0.5000i
0 − 0.5000i



0
0



0
0



0
0







(:, :, 3) =










0
0



   0.5000
0.5000



0
0



0
0



0
0



   0.5000
−0.5000



0
0



0
0







(:, :, 4) =










0
0



   0.5000
0.5000



0
0



0
0



0
0



0 + 0.5000i
0 − 0.5000i



0
0



0
0







(:, :, 5) =










0
0



0
0



   0.5000
0.5000



0
0



0
0



0
0



   0.5000
−0.5000



0
0







(:, :, 6) =










0
0



0
0



   0.5000
0.5000



0
0



0
0



0
0



0 + 0.5000i
0 − 0.5000i



0
0







(:, :, 7) =










0
0



0
0



0
0



   0.5000
0.5000



0
0



0
0



0
0



   0.5000
−0.5000







(:, :, 8) =










0
0



0
0



0
0



   0.5000
0.5000



0
0



0
0



0
0



0 + 0.5000i
0 − 0.5000i







(:, :, 9) =










   0.5000
0



0
0.5000



0
0



0
0



   0.5000
0



0
−0.5000



0
0



0
0







(:, :, 10) =










   0.5000
0



0
0.5000



0
0



0
0



0 + 0.5000i
0



0
0 − 0.5000i



0
0



0
0







(:, :, 11) =










0
0



   0.5000
0



0
0.5000



0
0



0
0



   0.5000
0



0
−0.5000



0
0







(:, :, 12) =










0
0



   0.5000
0



0
0.5000



0
0



0
0



0 + 0.5000i
0



0
0 − 0.5000i



0
0







(:, :, 13) =










   0.5000
0



0
0



0
0



0
0.5000



   0.5000
0



0
0



0
0



0
−0.5000







(:, :, 14) =










   0.5000
0



0
0



0
0



0
0.5000



0 + 0.5000i
0



0
0



0
0



0
0 − 0.5000i







(:, :, 15) =










0
0



   0.5000
0



0
0



0
0.5000



0
0



   0.5000
0



0
0



0
−0.5000







(:, :, 16) =










0
0



   0.5000
0



0
0



0
0.5000



0
0



0 + 0.5000i
0



0
0



0
0 − 0.5000i











- Rank 3





(:, :, 1) =









0.4082
0.4082
0


0
0
0


0
0
0


0
0
0


0
0
0.4082


0
0
0


0
0
0


0
0
0


0.4082
−0.4082
0


0
0
0


0
0
0


0
0
0


0
0
−0.4082


0
0
0


0
0
0


0
0
0







(:, :, 2) =









0
0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
0.4082


0
0
0


0
0
0


0
0
0


0
−0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
−0.4082


0
0
0


0
0
0


0
0
0







(:, :, 3) =









0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0


0
0
0







(:, :, 4) =









0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0







(:, :, 5) =









0
0
0


0.4082
0.4082
0


0
0
0


0
0
0


0
0
0


0
0
0.4082


0
0
0


0
0
0


0
0
0


0.4082
−0.4082
0


0
0
0


0
0
0


0
0
0


0
0
−0.4082


0
0
0


0
0
0







(:, :, 6) =









0
0
0


0
0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
0.4082


0
0
0


0
0
0


0
0
0


0
−0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
−0.4082


0
0
0


0
0
0







(:, :, 7) =









0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0







(:, :, 8) =









0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0







(:, :, 9) =









0
0
0


0
0
0


0.4082
0.4082
0


0
0
0


0
0
0


0
0
0


0
0
0.4082


0
0
0


0
0
0


0
0
0


0.4082
−0.4082
0


0
0
0


0
0
0


0
0
0


0
0
−0.4082


0
0
0







(:, :, 10) =









0
0
0


0
0
0


0
0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
0.4082


0
0
0


0
0
0


0
0
0


0
−0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
−0.4082


0
0
0







(:, :, 11) =









0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0







(:, :, 12) =









0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0







(:, :, 13) =









0
0
0


0
0
0


0
0
0


0.4082
0.4082
0


0
0
0


0
0
0


0
0
0


0
0
0.4082


0
0
0


0
0
0


0
0
0


0.4082
−0.4082
0


0
0
0


0
0
0


0
0
0


0
0
−0.4082







(:, :, 14) =









0
0
0


0
0
0


0
0
0


0
0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
0.4082


0
0
0


0
0
0


0
0
0


0
−0.4082
0


0
0
0


0
0
0


0
0
0


0.4082
0
−0.4082







(:, :, 15) =









0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082







(:, :, 16) =









0
0
0


0
0
0


0
0
0


0
0.4082
0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0


0
0
0


0
0
0


0
0
0


0
0.4082
−0.4082


0
0
0


0
0
0


0
0
0


0.4082
0
0










- Rank 4





(:, :, 1) =












   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
−0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
−0.3536



0
0
0
0



0
0
0
0



0
0
0
0







(:, :, 2) =












   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



0 + 0.3536i
0
0 − 0.3536i
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0 + 0.3536i
0
0 − 0.3536i



0
0
0
0



0
0
0
0



0
0
0
0







(:, :, 3) =












0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
−0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
−0.3536



0
0
0
0



0
0
0
0







(:, :, 4) =












0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



0 + 0.3536i
0
0 − 0.3536i
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0 + 0.3536i
0
0 − 0.3536i



0
0
0
0



0
0
0
0







(:, :, 5) =












0
0
0
0



0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
−0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
−0.3536



0
0
0
0







(:, :, 6) =












0
0
0
0



0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



0 + 0.3536i
0
0 − 0.3536i
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0 + 0.3536i
0
0 − 0.3536i



0
0
0
0







(:, :, 7) =












0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
−0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
−0.3536







(:, :, 8) =












0
0
0
0



0
0
0
0



0
0
0
0



   0.3536
0
0.3536
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0.3536
0
0.3536



0
0
0
0



0
0
0
0



0
0
0
0



0 + 0.3536i
0
0 − 0.3536i
0



0
0
0
0



0
0
0
0



0
0
0
0



0
0 + 0.3536i
0
0 − 0.3536i











- Rank 5





(:, :, 1) =











0.3162
0.3162
0
0
0


0
0
0.3162
0.3162
0


0
0
0
0
0.3162


0
0
0
0
0


0.3162
−0.3162
0
0
0


0
0
0.3162
−0.3162
0


0
0
0
0
0.3162


0
0
0
0
0










- Rank 6





(:, :, 1) =

















0.2887
0.2887
0
0
0
0



0   
0
0.2887
0.2887
0
0



0   
0
0
0
0.2887
0.2887



0   
0
0
0
0
0



0.2887
−0.2887
0
0
0
0



0   
0
0.2887
−0.2887
0
0



0   
0
0
0
0.2887
−0.2887



0   
0
0
0
0
0











- Rank 7





(:, :, 1) =


columns 1-4















   0.2673
0.2673
0
0



0
0
0.2673
0.2673



0
0
0
0



0
0
0
0



   0.2673
−0.2673
0
0



0
0
0.2673
−0.2673



0
0
0
0



0
0
0
0











columns 5-7












0
0
0


0
0
0


0.2673
0.2673
0


0
0
0.2673


0
0
0


0
0
0


0.2673
−0.2673
0


0
0
0.2673










- Rank 8





(:, :, 1) =


columns 1-4












   0.2500
0.2500
0
0



0
0
0.2500
0.2500



0
0
0
0



0
0
0
0



   0.2500
−0.2500
0
0



0
0
0.2500
−0.2500



0
0
0
0



0
0
0
0







columns 5-8












0
0
0
0



0
0
0
0



   0.2500
0.2500
0
0



0
0
0.2500
0.2500



0
0
0
0



0
0
0
0



   0.2500
−0.2500
0
0



0
0
0.2500
−0.2500










Detailed Digits of Overall Codebook C
A final precoding matrix candidate may be induced by performing inner product with respect to one of codewords belonging to the first codebook C1 and one of codewords belonging to the second codebook C2. That is, the receiver may select a single codeword from the codewords belonging to the first codebook C1 and may select a single codeword from the codewords belonging to the second codebook C2. A combination of the selected two codewords may indicate one of codewords belonging to the overall codebook C, which is described below.
Hereinafter, ans(;,;m,n) for rank r may indicate an inter product between ans(;,;m) in the first codebook C1 for rank r and (;,;,n) in the second codebook C2 for rank r. That is, ans(;,;m,n)=ans(;,;m) (;,;,n).
For a variety of ranks, the detailed digits of the overall codebook C may be expressed as follows:












Rank 1





ans(:, :, 1, 1) =


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


ans(:, :, 2, 1) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


ans(:, :, 3, 1) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


ans(:, :, 4, 1) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


ans(:, :, 5, 1) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


ans(:, :, 6, 1) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


ans(:, :, 7, 1) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


ans(:, :, 8, 1) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


ans(:, :, 9, 1) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


ans(:, :, 10, 1) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


ans(:, :, 11, 1) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


ans(:, :, 12, 1) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


ans(:, :, 13, 1) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


ans(:, :, 14, 1) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


ans(:, :, 15, 1) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


ans(:, :, 16, 1) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


ans(:, :, 1, 2) =


  0.3536


  0.3536


  0.3536


  0.3536


     0 + 0.3536i


     0 + 0.3536i


     0 + 0.3536i


     0 + 0.3536i


ans(:, :, 2, 2) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


     0 + 0.3536i


−0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 + 0.1353i


ans(:, :, 3, 2) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


     0 + 0.3536i


−0.2500 + 0.2500i


−0.3536 + 0.0000i


−0.2500 − 0.2500i


ans(:, :, 4, 2) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


     0 + 0.3536i


−0.3266 + 0.1353i


−0.2500 − 0.2500i


  0.1353 − 0.3266i


ans(:, :, 5, 2) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


     0 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


  0.3536 − 0.0000i


ans(:, :, 6, 2) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


     0 + 0.3536i


−0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 + 0.3266i


ans(:, :, 7, 2) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


     0 + 0.3536i


−0.2500 − 0.2500i


  0.3536 − 0.0000i


−0.2500 + 0.2500i


ans(:, :, 8, 2) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


     0 + 0.3536i


−0.1353 − 0.3266i


  0.2500 + 0.2500i


−0.3266 − 0.1353i


ans(:, :, 9, 2) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


     0 + 0.3536i


−0.0000 − 0.3536i


  0.0000 + 0.3536i


−0.0000 − 0.3536i


ans(:, :, 10, 2) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


     0 + 0.3536i


  0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 − 0.1353i


ans(:, :, 11, 2) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


     0 + 0.3536i


  0.2500 − 0.2500i


−0.3536 + 0.0000i


  0.2500 + 0.2500i


ans(:, :, 12, 2) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


     0 + 0.3536i


  0.3266 − 0.1353i


−0.2500 − 0.2500i


−0.1353 + 0.3266i


ans(:, :, 13, 2) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


     0 + 0.3536i


  0.3536 − 0.0000i


−0.0000 − 0.3536i


−0.3536 + 0.0000i


ans(:, :, 14, 2) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


     0 + 0.3536i


  0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 − 0.3266i


ans(:, :, 15, 2) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


     0 + 0.3536i


  0.2500 + 0.2500i


  0.3536 − 0.0000i


  0.2500 − 0.2500i


ans(:, :, 16, 2) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


     0 + 0.3536i


  0.1353 + 0.3266i


  0.2500 + 0.2500i


  0.3266 + 0.1353i


ans(:, :, 1, 3) =


  0.3536


  0.3536


  0.3536


  0.3536


−0.3536


−0.3536


−0.3536


−0.3536


ans(:, :, 2, 3) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


−0.3536


−0.3266 − 0.1353i


−0.2500 − 0.2500i


−0.1353 − 0.3266i


ans(:, :, 3, 3) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


−0.3536


−0.2500 − 0.2500i


−0.0000 − 0.3536i


  0.2500 − 0.2500i


ans(:, :, 4, 3) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


−0.3536


−0.1353 − 0.3266i


  0.2500 − 0.2500i


  0.3266 + 0.1353i


ans(:, :, 5, 3) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


−0.3536


−0.0000 − 0.3536i


  0.3536 − 0.0000i


  0.0000 + 0.3536i


ans(:, :, 6, 3) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


−0.3536


  0.1353 − 0.3266i


  0.2500 + 0.2500i


−0.3266 + 0.1353i


ans(:, :, 7, 3) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


−0.3536


  0.2500 − 0.2500i


  0.0000 + 0.3536i


−0.2500 − 0.2500i


ans(:, :, 8, 3) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


−0.3536


  0.3266 − 0.1353i


−0.2500 + 0.2500i


  0.1353 − 0.3266i


ans(:, :, 9, 3) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


−0.3536


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536 − 0.0000i


ans(:, :, 10, 3) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


−0.3536


  0.3266 + 0.1353i


−0.2500 − 0.2500i


  0.1353 + 0.3266i


ans(:, :, 11, 3) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


−0.3536


  0.2500 + 0.2500i


−0.0000 − 0.3536i


−0.2500 + 0.2500i


ans(:, :, 12, 3) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


−0.3536


  0.1353 + 0.3266i


  0.2500 − 0.2500i


−0.3266 − 0.1353i


ans(:, :, 13, 3) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


−0.3536


  0.0000 + 0.3536i


  0.3536 − 0.0000i


−0.0000 − 0.3536i


ans(:, :, 14, 3) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


−0.3536


−0.1353 + 0.3266i


  0.2500 + 0.2500i


  0.3266 − 0.1353i


ans(:, :, 15, 3) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


−0.3536


−0.2500 + 0.2500i


  0.0000 + 0.3536i


  0.2500 + 0.2500i


ans(:, :, 16, 3) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


−0.3536


−0.3266 + 0.1353i


−0.2500 + 0.2500i


−0.1353 + 0.3266i


ans(:, :, 1, 4) =


  0.3536


  0.3536


  0.3536


  0.3536


     0 − 0.3536i


     0 − 0.3536i


     0 − 0.3536i


     0 − 0.3536i


ans(:, :, 2, 4) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


     0 − 0.3536i


  0.1353 − 0.3266i


  0.2500 − 0.2500i


  0.3266 − 0.1353i


ans(:, :, 3, 4) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


     0 − 0.3536i


  0.2500 − 0.2500i


  0.3536 − 0.0000i


  0.2500 + 0.2500i


ans(:, :, 4, 4) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


     0 − 0.3536i


  0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 + 0.3266i


ans(:, :, 5, 4) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


     0 − 0.3536i


  0.3536 − 0.0000i


  0.0000 + 0.3536i


−0.3536 + 0.0000i


ans(:, :, 6, 4) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


     0 − 0.3536i


  0.3266 + 0.1353i


−0.2500 + 0.2500i


−0.1353 − 0.3266i


ans(:, :, 7, 4) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


     0 − 0.3536i


  0.2500 + 0.2500i


−0.3536 + 0.0000i


  0.2500 − 0.2500i


ans(:, :, 8, 4) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


     0 − 0.3536i


  0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 + 0.1353i


ans(:, :, 9, 4) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


     0 − 0.3536i


  0.0000 + 0.3536i


−0.0000 − 0.3536i


  0.0000 + 0.3536i


ans(:, :, 10, 4) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


     0 − 0.3536i


−0.1353 + 0.3266i


  0.2500 − 0.2500i


−0.3266 + 0.1353i


ans(:, :, 11, 4) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


     0 − 0.3536i


−0.2500 + 0.2500i


  0.3536 − 0.0000i


−0.2500 − 0.2500i


ans(:, :, 12, 4) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


     0 − 0.3536i


−0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 − 0.3266i


ans(:, :, 13, 4) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


     0 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


  0.3536 − 0.0000i


ans(:, :, 14, 4) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


     0 − 0.3536i


−0.3266 − 0.1353i


−0.2500 + 0.2500i


  0.1353 + 0.3266i


ans(:, :, 15, 4) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


     0 − 0.3536i


−0.2500 − 0.2500i


−0.3536 + 0.0000i


−0.2500 + 0.2500i


ans(:, :, 16, 4) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


     0 − 0.3536i


−0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 − 0.1353i


ans(:, :, 1, 5) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


ans(:, :, 2, 5) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


ans(:, :, 3, 5) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


ans(:, :, 4, 5) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


ans(:, :, 5, 5) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


ans(:, :, 6, 5) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


ans(:, :, 7, 5) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


ans(:, :, 8, 5) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


ans(:, :, 9, 5) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


ans(:, :, 10, 5) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


ans(:, :, 11, 5) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


ans(:, :, 12, 5) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


ans(:, :, 13, 5) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


ans(:, :, 14, 5) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


ans(:, :, 15, 5) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


ans(:, :, 16, 5) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


ans(:, :, 1, 6) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


     0 + 0.3536i


−0.0690 + 0.3468i


−0.1353 + 0.3266i


−0.1964 + 0.2940i


ans(:, :, 2, 6) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


     0 + 0.3536i


−0.1964 + 0.2940i


−0.3266 + 0.1353i


−0.3468 − 0.0690i


ans(:, :, 3, 6) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


     0 + 0.3536i


−0.2940 + 0.1964i


−0.3266 − 0.1353i


−0.0690 − 0.3468i


ans(:, :, 4, 6) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


     0 + 0.3536i


−0.3468 + 0.0690i


−0.1353 − 0.3266i


  0.2940 − 0.1964i


ans(:, :, 5, 6) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


     0 + 0.3536i


−0.3468 − 0.0690i


  0.1353 − 0.3266i


  0.2940 + 0.1964i


ans(:, :, 6, 6) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


     0 + 0.3536i


−0.2940 − 0.1964i


  0.3266 − 0.1353i


−0.0690 + 0.3468i


ans(:, :, 7, 6) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


     0 + 0.3536i


−0.1964 − 0.2940i


  0.3266 + 0.1353i


−0.3468 + 0.0690i


ans(:, :, 8, 6) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


     0 + 0.3536i


−0.0690 − 0.3468i


  0.1353 + 0.3266i


−0.1964 − 0.2940i


ans(:, :, 9, 6) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


     0 + 0.3536i


  0.0690 − 0.3468i


−0.1353 + 0.3266i


  0.1964 − 0.2940i


ans(:, :, 10, 6) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


     0 + 0.3536i


  0.1964 − 0.2940i


−0.3266 + 0.1353i


  0.3468 + 0.0690i


ans(:, :, 11, 6) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


     0 + 0.3536i


  0.2940 − 0.1964i


−0.3266 − 0.1353i


  0.0690 + 0.3468i


ans(:, :, 12, 6) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


     0 + 0.3536i


  0.3468 − 0.0690i


−0.1353 − 0.3266i


−0.2940 + 0.1964i


ans(:, :, 13, 6) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


     0 + 0.3536i


  0.3468 + 0.0690i


  0.1353 − 0.3266i


−0.2940 − 0.1964i


ans(:, :, 14, 6) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


     0 + 0.3536i


  0.2940 + 0.1964i


  0.3266 − 0.1353i


  0.0690 − 0.3468i


ans(:, :, 15, 6) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


     0 + 0.3536i


  0.1964 + 0.2940i


  0.3266 + 0.1353i


  0.3468 − 0.0690i


ans(:, :, 16, 6) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


     0 + 0.3536i


  0.0690 + 0.3468i


  0.1353 + 0.3266i


  0.1964 + 0.2940i


ans(:, :, 1, 7) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


−0.3536


−0.3468 − 0.0690i


−0.3266 − 0.1353i


−0.2940 − 0.1964i


ans(:, :, 2, 7) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


−0.3536


−0.2940 − 0.1964i


−0.1353 − 0.3266i


  0.0690 − 0.3468i


ans(:, :, 3, 7) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


−0.3536


−0.1964 − 0.2940i


  0.1353 − 0.3266i


  0.3468 − 0.0690i


ans(:, :, 4, 7) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


−0.3536


−0.0690 − 0.3468i


  0.3266 − 0.1353i


  0.1964 + 0.2940i


ans(:, :, 5, 7) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


−0.3536


  0.0690 − 0.3468i


  0.3266 + 0.1353i


−0.1964 + 0.2940i


ans(:, :, 6, 7) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


−0.3536


  0.1964 − 0.2940i


  0.1353 + 0.3266i


−0.3468 − 0.0690i


ans(:, :, 7, 7) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


−0.3536


  0.2940 − 0.1964i


−0.1353 + 0.3266i


−0.0690 − 0.3468i


ans(:, :, 8, 7) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


−0.3536


  0.3468 − 0.0690i


−0.3266 + 0.1353i


  0.2940 − 0.1964i


ans(:, :, 9, 7) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


−0.3536


  0.3468 + 0.0690i


−0.3266 − 0.1353i


  0.2940 + 0.1964i


ans(:, :, 10, 7) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


−0.3536


  0.2940 + 0.1964i


−0.1353 − 0.3266i


−0.0690 + 0.3468i


ans(:, :, 11, 7) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


−0.3536


  0.1964 + 0.2940i


  0.1353 − 0.3266i


−0.3468 + 0.0690i


ans(:, :, 12, 7) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


−0.3536


  0.0690 + 0.3468i


  0.3266 − 0.1353i


−0.1964 − 0.2940i


ans(:, :, 13, 7) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


−0.3536


−0.0690 + 0.3468i


  0.3266 + 0.1353i


  0.1964 − 0.2940i


ans(:, :, 14, 7) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


−0.3536


−0.1964 + 0.2940i


  0.1353 + 0.3266i


  0.3468 + 0.0690i


ans(:, :, 15, 7) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


−0.3536


−0.2940 + 0.1964i


−0.1353 + 0.3266i


  0.0690 + 0.3468i


ans(:, :, 16, 7) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


−0.3536


−0.3468 + 0.0690i


−0.3266 + 0.1353i


−0.2940 + 0.1964i


ans(:, :, 1, 8) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


     0 − 0.3536i


  0.0690 − 0.3468i


  0.1353 − 0.3266i


  0.1964 − 0.2940i


ans(:, :, 2, 8) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


     0 − 0.3536i


  0.1964 − 0.2940i


  0.3266 − 0.1353i


  0.3468 + 0.0690i


ans(:, :, 3, 8) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


     0 − 0.3536i


  0.2940 − 0.1964i


  0.3266 + 0.1353i


  0.0690 + 0.3468i


ans(:, :, 4, 8) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


     0 − 0.3536i


  0.3468 − 0.0690i


  0.1353 + 0.3266i


−0.2940 + 0.1964i


ans(:, :, 5, 8) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


     0 − 0.3536i


  0.3468 + 0.0690i


−0.1353 + 0.3266i


−0.2940 − 0.1964i


ans(:, :, 6, 8) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


     0 − 0.3536i


  0.2940 + 0.1964i


−0.3266 + 0.1353i


  0.0690 − 0.3468i


ans(:, :, 7, 8) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


     0 − 0.3536i


  0.1964 + 0.2940i


−0.3266 − 0.1353i


  0.3468 − 0.0690i


ans(:, :, 8, 8) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


     0 − 0.3536i


  0.0690 + 0.3468i


−0.1353 − 0.3266i


  0.1964 + 0.2940i


ans(:, :, 9, 8) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


     0 − 0.3536i


−0.0690 + 0.3468i


  0.1353 − 0.3266i


−0.1964 + 0.2940i


ans(:, :, 10, 8) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


     0 − 0.3536i


−0.1964 + 0.2940i


  0.3266 − 0.1353i


−0.3468 − 0.0690i


ans(:, :, 11, 8) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


     0 − 0.3536i


−0.2940 + 0.1964i


  0.3266 + 0.1353i


−0.0690 − 0.3468i


ans(:, :, 12, 8) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


     0 − 0.3536i


−0.3468 + 0.0690i


  0.1353 + 0.3266i


  0.2940 − 0.1964i


ans(:, :, 13, 8) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


     0 − 0.3536i


−0.3468 − 0.0690i


−0.1353 + 0.3266i


  0.2940 + 0.1964i


ans(:, :, 14, 8) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


     0 − 0.3536i


−0.2940 − 0.1964i


−0.3266 + 0.1353i


−0.0690 + 0.3468i


ans(:, :, 15, 8) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


     0 − 0.3536i


−0.1964 − 0.2940i


−0.3266 − 0.1353i


−0.3468 + 0.0690i


ans(:, :, 16, 8) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


     0 − 0.3536i


−0.0690 − 0.3468i


−0.1353 − 0.3266i


−0.1964 − 0.2940i


ans(:, :, 1, 9) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


ans(:, :, 2, 9) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


ans(:, :, 3, 9) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


ans(:, :, 4, 9) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


ans(:, :, 5, 9) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


ans(:, :, 6, 9) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


ans(:, :, 7, 9) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


ans(:, :, 8, 9) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


ans(:, :, 9, 9) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


ans(:, :, 10, 9) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


ans(:, :, 11, 9) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


ans(:, :, 12, 9) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


ans(:, :, 13, 9) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


ans(:, :, 14, 9) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


ans(:, :, 15, 9) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


ans(:, :, 16, 9) =


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


ans(:, :, 1, 10) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


     0 + 0.3536i


−0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 + 0.1353i


ans(:, :, 2, 10) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


     0 + 0.3536i


−0.2500 + 0.2500i


−0.3536 + 0.0000i


−0.2500 − 0.2500i


ans(:, :, 3, 10) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


     0 + 0.3536i


−0.3266 + 0.1353i


−0.2500 − 0.2500i


  0.1353 − 0.3266i


ans(:, :, 4, 10) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


     0 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


  0.3536 − 0.0000i


ans(:, :, 5, 10) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


     0 + 0.3536i


−0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 + 0.3266i


ans(:, :, 6, 10) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


     0 + 0.3536i


−0.2500 − 0.2500i


  0.3536 − 0.0000i


−0.2500 + 0.2500i


ans(:, :, 7, 10) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


     0 + 0.3536i


−0.1353 − 0.3266i


  0.2500 + 0.2500i


−0.3266 − 0.1353i


ans(:, :, 8, 10) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


     0 + 0.3536i


−0.0000 − 0.3536i


  0.0000 + 0.3536i


−0.0000 − 0.3536i


ans(:, :, 9, 10) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


     0 + 0.3536i


  0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 − 0.1353i


ans(:, :, 10, 10) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


     0 + 0.3536i


  0.2500 − 0.2500i


−0.3536 + 0.0000i


  0.2500 + 0.2500i


ans(:, :, 11, 10) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


     0 + 0.3536i


  0.3266 − 0.1353i


−0.2500 − 0.2500i


−0.1353 + 0.3266i


ans(:, :, 12, 10) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


     0 + 0.3536i


  0.3536 − 0.0000i


−0.0000 − 0.3536i


−0.3536 + 0.0000i


ans(:, :, 13, 10) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


     0 + 0.3536i


  0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 − 0.3266i


ans(:, :, 14, 10) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


     0 + 0.3536i


  0.2500 + 0.2500i


  0.3536 − 0.0000i


  0.2500 − 0.2500i


ans(:, :, 15, 10) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


     0 + 0.3536i


  0.1353 + 0.3266i


  0.2500 + 0.2500i


  0.3266 + 0.1353i


ans(:, :, 16, 10) =


  0.3536


  0.3536


  0.3536


  0.3536


     0 + 0.3536i


     0 + 0.3536i


     0 + 0.3536i


     0 + 0.3536i


ans(:, :, 1, 11) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


−0.3536


−0.3266 − 0.1353i


−0.2500 − 0.2500i


−0.1353 − 0.3266i


ans(:, :, 2, 11) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


−0.3536


−0.2500 − 0.2500i


−0.0000 − 0.3536i


  0.2500 − 0.2500i


ans(:, :, 3, 11) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


−0.3536


−0.1353 − 0.3266i


  0.2500 − 0.2500i


  0.3266 + 0.1353i


ans(:, :, 4, 11) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


−0.3536


−0.0000 − 0.3536i


  0.3536 − 0.0000i


  0.0000 + 0.3536i


ans(:, :, 5, 11) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


−0.3536


  0.1353 − 0.3266i


  0.2500 + 0.2500i


−0.3266 + 0.1353i


ans(:, :, 6, 11) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


−0.3536


  0.2500 − 0.2500i


  0.0000 + 0.3536i


−0.2500 − 0.2500i


ans(:, :, 7, 11) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


−0.3536


  0.3266 − 0.1353i


−0.2500 + 0.2500i


  0.1353 − 0.3266i


ans(:, :, 8, 11) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


−0.3536


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536 − 0.0000i


ans(:, :, 9, 11) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


−0.3536


  0.3266 + 0.1353i


−0.2500 − 0.2500i


  0.1353 + 0.3266i


ans(:, :, 10, 11) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


−0.3536


  0.2500 + 0.2500i


−0.0000 − 0.3536i


−0.2500 + 0.2500i


ans(:, :, 11, 11) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


−0.3536


  0.1353 + 0.3266i


  0.2500 − 0.2500i


−0.3266 − 0.1353i


ans(:, :, 12, 11) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


−0.3536


  0.0000 + 0.3536i


  0.3536 − 0.0000i


−0.0000 − 0.3536i


ans(:, :, 13, 11) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


−0.3536


−0.1353 + 0.3266i


  0.2500 + 0.2500i


  0.3266 − 0.1353i


ans(:, :, 14, 11) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


−0.3536


−0.2500 + 0.2500i


  0.0000 + 0.3536i


  0.2500 + 0.2500i


ans(:, :, 15, 11) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


−0.3536


−0.3266 + 0.1353i


−0.2500 + 0.2500i


−0.1353 + 0.3266i


ans(:, :, 16, 11) =


  0.3536


  0.3536


  0.3536


  0.3536


−0.3536


−0.3536


−0.3536


−0.3536


ans(:, :, 1, 12) =


  0.3536


  0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 + 0.3266i


     0 − 0.3536i


  0.1353 − 0.3266i


  0.2500 − 0.2500i


  0.3266 − 0.1353i


ans(:, :, 2, 12) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


     0 − 0.3536i


  0.2500 − 0.2500i


  0.3536 − 0.0000i


  0.2500 + 0.2500i


ans(:, :, 3, 12) =


  0.3536


  0.1353 + 0.3266i


−0.2500 + 0.2500i


−0.3266 − 0.1353i


     0 − 0.3536i


  0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 + 0.3266i


ans(:, :, 4, 12) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


     0 − 0.3536i


  0.3536 − 0.0000i


  0.0000 + 0.3536i


−0.3536 + 0.0000i


ans(:, :, 5, 12) =


  0.3536


−0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 − 0.1353i


     0 − 0.3536i


  0.3266 + 0.1353i


−0.2500 + 0.2500i


−0.1353 − 0.3266i


ans(:, :, 6, 12) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


     0 − 0.3536i


  0.2500 + 0.2500i


−0.3536 + 0.0000i


  0.2500 − 0.2500i


ans(:, :, 7, 12) =


  0.3536


−0.3266 + 0.1353i


  0.2500 − 0.2500i


−0.1353 + 0.3266i


     0 − 0.3536i


  0.1353 + 0.3266i


−0.2500 − 0.2500i


  0.3266 + 0.1353i


ans(:, :, 8, 12) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


     0 − 0.3536i


  0.0000 + 0.3536i


−0.0000 − 0.3536i


  0.0000 + 0.3536i


ans(:, :, 9, 12) =


  0.3536


−0.3266 − 0.1353i


  0.2500 + 0.2500i


−0.1353 − 0.3266i


     0 − 0.3536i


−0.1353 + 0.3266i


  0.2500 − 0.2500i


−0.3266 + 0.1353i


ans(:, :, 10, 12) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


     0 − 0.3536i


−0.2500 + 0.2500i


  0.3536 − 0.0000i


−0.2500 − 0.2500i


ans(:, :, 11, 12) =


  0.3536


−0.1353 − 0.3266i


−0.2500 + 0.2500i


  0.3266 + 0.1353i


     0 − 0.3536i


−0.3266 + 0.1353i


  0.2500 + 0.2500i


  0.1353 − 0.3266i


ans(:, :, 12, 12) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


     0 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


  0.3536 − 0.0000i


ans(:, :, 13, 12) =


  0.3536


  0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 + 0.1353i


     0 − 0.3536i


−0.3266 − 0.1353i


−0.2500 + 0.2500i


  0.1353 + 0.3266i


ans(:, :, 14, 12) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


     0 − 0.3536i


−0.2500 − 0.2500i


−0.3536 + 0.0000i


−0.2500 + 0.2500i


ans(:, :, 15, 12) =


  0.3536


  0.3266 − 0.1353i


  0.2500 − 0.2500i


  0.1353 − 0.3266i


     0 − 0.3536i


−0.1353 − 0.3266i


−0.2500 − 0.2500i


−0.3266 − 0.1353i


ans(:, :, 16, 12) =


  0.3536


  0.3536


  0.3536


  0.3536


     0 − 0.3536i


     0 − 0.3536i


     0 − 0.3536i


     0 − 0.3536i


ans(:, :, 1, 13) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


ans(:, :, 2, 13) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


ans(:, :, 3, 13) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


ans(:, :, 4, 13) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


ans(:, :, 5, 13) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


ans(:, :, 6, 13) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


ans(:, :, 7, 13) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


ans(:, :, 8, 13) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


ans(:, :, 9, 13) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


ans(:, :, 10, 13) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


ans(:, :, 11, 13) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


ans(:, :, 12, 13) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


ans(:, :, 13, 13) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


ans(:, :, 14, 13) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


ans(:, :, 15, 13) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


ans(:, :, 16, 13) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


ans(:, :, 1, 14) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


     0 + 0.3536i


−0.1964 + 0.2940i


−0.3266 + 0.1353i


−0.3468 − 0.0690i


ans(:, :, 2, 14) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


     0 + 0.3536i


−0.2940 + 0.1964i


−0.3266 − 0.1353i


−0.0690 − 0.3468i


ans(:, :, 3, 14) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


     0 + 0.3536i


−0.3468 + 0.0690i


−0.1353 − 0.3266i


  0.2940 − 0.1964i


ans(:, :, 4, 14) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


     0 + 0.3536i


−0.3468 − 0.0690i


  0.1353 − 0.3266i


  0.2940 + 0.1964i


ans(:, :, 5, 14) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


     0 + 0.3536i


−0.2940 − 0.1964i


  0.3266 − 0.1353i


−0.0690 + 0.3468i


ans(:, :, 6, 14) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


     0 + 0.3536i


−0.1964 − 0.2940i


  0.3266 + 0.1353i


−0.3468 + 0.0690i


ans(:, :, 7, 14) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


     0 + 0.3536i


−0.0690 − 0.3468i


  0.1353 + 0.3266i


−0.1964 − 0.2940i


ans(:, :, 8, 14) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


     0 + 0.3536i


  0.0690 − 0.3468i


−0.1353 + 0.3266i


  0.1964 − 0.2940i


ans(:, :, 9, 14) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


     0 + 0.3536i


  0.1964 − 0.2940i


−0.3266 + 0.1353i


  0.3468 + 0.0690i


ans(:, :, 10, 14) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


     0 + 0.3536i


  0.2940 − 0.1964i


−0.3266 − 0.1353i


  0.0690 + 0.3468i


ans(:, :, 11, 14) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


     0 + 0.3536i


  0.3468 − 0.0690i


−0.1353 − 0.3266i


−0.2940 + 0.1964i


ans(:, :, 12, 14) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


     0 + 0.3536i


  0.3468 + 0.0690i


  0.1353 − 0.3266i


−0.2940 − 0.1964i


ans(:, :, 13, 14) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


     0 + 0.3536i


  0.2940 + 0.1964i


  0.3266 − 0.1353i


  0.0690 − 0.3468i


ans(:, :, 14, 14) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


     0 + 0.3536i


  0.1964 + 0.2940i


  0.3266 + 0.1353i


  0.3468 − 0.0690i


ans(:, :, 15, 14) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


     0 + 0.3536i


  0.0690 + 0.3468i


  0.1353 + 0.3266i


  0.1964 + 0.2940i


ans(:, :, 16, 14) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


     0 + 0.3536i


−0.0690 + 0.3468i


−0.1353 + 0.3266i


−0.1964 + 0.2940i


ans(:, :, 1, 15) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


−0.3536


−0.2940 − 0.1964i


−0.1353 − 0.3266i


  0.0690 − 0.3468i


ans(:, :, 2, 15) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


−0.3536


−0.1964 − 0.2940i


  0.1353 − 0.3266i


  0.3468 − 0.0690i


ans(:, :, 3, 15) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


−0.3536


−0.0690 − 0.3468i


  0.3266 − 0.1353i


  0.1964 + 0.2940i


ans(:, :, 4, 15) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


−0.3536


  0.0690 − 0.3468i


  0.3266 + 0.1353i


−0.1964 + 0.2940i


ans(:, :, 5, 15) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


−0.3536


  0.1964 − 0.2940i


  0.1353 + 0.3266i


−0.3468 − 0.0690i


ans(:, :, 6, 15) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


−0.3536


  0.2940 − 0.1964i


−0.1353 + 0.3266i


−0.0690 − 0.3468i


ans(:, :, 7, 15) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


−0.3536


  0.3468 − 0.0690i


−0.3266 + 0.1353i


  0.2940 − 0.1964i


ans(:, :, 8, 15) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


−0.3536


  0.3468 + 0.0690i


−0.3266 − 0.1353i


  0.2940 + 0.1964i


ans(:, :, 9, 15) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


−0.3536


  0.2940 + 0.1964i


−0.1353 − 0.3266i


−0.0690 + 0.3468i


ans(:, :, 10, 15) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


−0.3536


  0.1964 + 0.2940i


  0.1353 − 0.3266i


−0.3468 + 0.0690i


ans(:, :, 11, 15) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


−0.3536


  0.0690 + 0.3468i


  0.3266 − 0.1353i


−0.1964 − 0.2940i


ans(:, :, 12, 15) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


−0.3536


−0.0690 + 0.3468i


  0.3266 + 0.1353i


  0.1964 − 0.2940i


ans(:, :, 13, 15) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


−0.3536


−0.1964 + 0.2940i


  0.1353 + 0.3266i


  0.3468 + 0.0690i


ans(:, :, 14, 15) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


−0.3536


−0.2940 + 0.1964i


−0.1353 + 0.3266i


  0.0690 + 0.3468i


ans(:, :, 15, 15) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


−0.3536


−0.3468 + 0.0690i


−0.3266 + 0.1353i


−0.2940 + 0.1964i


ans(:, :, 16, 15) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


−0.3536


−0.3468 − 0.0690i


−0.3266 − 0.1353i


−0.2940 − 0.1964i


ans(:, :, 1, 16) =


  0.3536


  0.2940 + 0.1964i


  0.1353 + 0.3266i


−0.0690 + 0.3468i


     0 − 0.3536i


  0.1964 − 0.2940i


  0.3266 − 0.1353i


  0.3468 + 0.0690i


ans(:, :, 2, 16) =


  0.3536


  0.1964 + 0.2940i


−0.1353 + 0.3266i


−0.3468 + 0.0690i


     0 − 0.3536i


  0.2940 − 0.1964i


  0.3266 + 0.1353i


  0.0690 + 0.3468i


ans(:, :, 3, 16) =


  0.3536


  0.0690 + 0.3468i


−0.3266 + 0.1353i


−0.1964 − 0.2940i


     0 − 0.3536i


  0.3468 − 0.0690i


  0.1353 + 0.3266i


−0.2940 + 0.1964i


ans(:, :, 4, 16) =


  0.3536


−0.0690 + 0.3468i


−0.3266 − 0.1353i


  0.1964 − 0.2940i


     0 − 0.3536i


  0.3468 + 0.0690i


−0.1353 + 0.3266i


−0.2940 − 0.1964i


ans(:, :, 5, 16) =


  0.3536


−0.1964 + 0.2940i


−0.1353 − 0.3266i


  0.3468 + 0.0690i


     0 − 0.3536i


  0.2940 + 0.1964i


−0.3266 + 0.1353i


  0.0690 − 0.3468i


ans(:, :, 6, 16) =


  0.3536


−0.2940 + 0.1964i


  0.1353 − 0.3266i


  0.0690 + 0.3468i


     0 − 0.3536i


  0.1964 + 0.2940i


−0.3266 − 0.1353i


  0.3468 − 0.0690i


ans(:, :, 7, 16) =


  0.3536


−0.3468 + 0.0690i


  0.3266 − 0.1353i


−0.2940 + 0.1964i


     0 − 0.3536i


  0.0690 + 0.3468i


−0.1353 − 0.3266i


  0.1964 + 0.2940i


ans(:, :, 8, 16) =


  0.3536


−0.3468 − 0.0690i


  0.3266 + 0.1353i


−0.2940 − 0.1964i


     0 − 0.3536i


−0.0690 + 0.3468i


  0.1353 − 0.3266i


−0.1964 + 0.2940i


ans(:, :, 9, 16) =


  0.3536


−0.2940 − 0.1964i


  0.1353 + 0.3266i


  0.0690 − 0.3468i


     0 − 0.3536i


−0.1964 + 0.2940i


  0.3266 − 0.1353i


−0.3468 − 0.0690i


ans(:, :, 10, 16) =


  0.3536


−0.1964 − 0.2940i


−0.1353 + 0.3266i


  0.3468 − 0.0690i


     0 − 0.3536i


−0.2940 + 0.1964i


  0.3266 + 0.1353i


−0.0690 − 0.3468i


ans(:, :, 11, 16) =


  0.3536


−0.0690 − 0.3468i


−0.3266 + 0.1353i


  0.1964 + 0.2940i


     0 − 0.3536i


−0.3468 + 0.0690i


  0.1353 + 0.3266i


  0.2940 − 0.1964i


ans(:, :, 12, 16) =


  0.3536


  0.0690 − 0.3468i


−0.3266 − 0.1353i


−0.1964 + 0.2940i


     0 − 0.3536i


−0.3468 − 0.0690i


−0.1353 + 0.3266i


  0.2940 + 0.1964i


ans(:, :, 13, 16) =


  0.3536


  0.1964 − 0.2940i


−0.1353 − 0.3266i


−0.3468 − 0.0690i


     0 − 0.3536i


−0.2940 − 0.1964i


−0.3266 + 0.1353i


−0.0690 + 0.3468i


ans(:, :, 14, 16) =


  0.3536


  0.2940 − 0.1964i


  0.1353 − 0.3266i


−0.0690 − 0.3468i


     0 − 0.3536i


−0.1964 − 0.2940i


−0.3266 − 0.1353i


−0.3468 + 0.0690i


ans(:, :, 15, 16) =


  0.3536


  0.3468 − 0.0690i


  0.3266 − 0.1353i


  0.2940 − 0.1964i


     0 − 0.3536i


−0.0690 − 0.3468i


−0.1353 − 0.3266i


−0.1964 − 0.2940i


ans(:, :, 16, 16) =


  0.3536


  0.3468 + 0.0690i


  0.3266 + 0.1353i


  0.2940 + 0.1964i


     0 − 0.3536i


  0.0690 − 0.3468i


  0.1353 − 0.3266i


  0.1964 − 0.2940i





- Rank 2





ans(:, :, 1, 1) =










  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
−0.2500



  0.2500
−0.2500



  0.2500
−0.2500



  0.2500
−0.2500







ans(:, :, 2, 1) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.2500
−0.2500



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 3, 1) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2500
−0.2500



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 4, 1) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.2500
−0.2500



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2310 − 0.0957i
  0.2310 + 0.0957i







ans(:, :, 5, 1) =










  0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.2500
−0.2500



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 6, 1) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2500
−0.2500



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 7, 1) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.2500
−0.2500



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 8, 1) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2500
−0.2500



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 + 0.2310i
  0.0957 − 0.2310i







ans(:, :, 9, 1) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500
−0.2500



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 10, 1) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2500
−0.2500



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.0957 − 0.2310i
  0.0957 + 0.2310i







ans(:, :, 11, 1) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.2500
−0.2500



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 12, 1) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2500
−0.2500



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



  0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 13, 1) =










  0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.2500
−0.2500



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.0000 + 0.2500i
−0.0000 − 0.2500i







ans(:, :, 14, 1) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.2500
−0.2500



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



−0.2310 + 0.0957i
  0.2310 − 0.0957i







ans(:, :, 15, 1) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2500
−0.2500



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 16, 1) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.2500
−0.2500



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



  0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 1, 2) =










  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i







ans(:, :, 2, 2) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2310 + 0.0957i
  0.2310 − 0.0957i







ans(:, :, 3, 2) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 4, 2) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 5, 2) =










  0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i







ans(:, :, 6, 2) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



  0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 7, 2) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 8, 2) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.2310 − 0.0957i
  0.2310 + 0.0957i







ans(:, :, 9, 2) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



     0 + 0.2500i
     0 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 10, 2) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



  0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 11, 2) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 12, 2) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



−0.0957 + 0.2310i
  0.0957 − 0.2310i







ans(:, :, 13, 2) =










  0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



     0 + 0.2500i
     0 − 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 14, 2) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 − 0.2310i
  0.0957 + 0.2310i







ans(:, :, 15, 2) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



  0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 16, 2) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 1, 3) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.2500
−0.2500



  0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.2079 + 0.1389i
−0.2079 − 0.1389i







ans(:, :, 2, 3) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.0488 + 0.2452i



  0.2500
−0.2500



  0.2079 + 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.0488 + 0.2452i
  0.0488 − 0.2452i







ans(:, :, 3, 3) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2500
−0.2500



  0.1389 + 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.2452 + 0.0488i
  0.2452 − 0.0488i







ans(:, :, 4, 3) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



−0.1389 − 0.2079i
−0.1389 − 0.2079i



  0.2500
−0.2500



  0.0488 + 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.1389 − 0.2079i
  0.1389 + 0.2079i







ans(:, :, 5, 3) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1389 − 0.2079i
  0.1389 − 0.2079i



  0.2500
−0.2500



−0.0488 + 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 6, 3) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2500
−0.2500



−0.1389 + 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 7, 3) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.0488 + 0.2452i
  0.0488 + 0.2452i



  0.2500
−0.2500



−0.2079 + 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 8, 3) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.2500
−0.2500



−0.2452 + 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.2079 + 0.1389i
  0.2079 − 0.1389i







ans(:, :, 9, 3) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.2500
−0.2500



−0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2079 − 0.1389i
  0.2079 + 0.1389i







ans(:, :, 10, 3) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.0488 − 0.2452i



  0.2500
−0.2500



−0.2079 − 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 11, 3) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2500
−0.2500



−0.1389 − 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 12, 3) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1389 + 0.2079i
  0.1389 + 0.2079i



  0.2500
−0.2500



−0.0488 − 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 13, 3) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.1389 + 0.2079i
−0.1389 + 0.2079i



  0.2500
−0.2500



  0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.1389 + 0.2079i
  0.1389 − 0.2079i







ans(:, :, 14, 3) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2500
−0.2500



  0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.2452 − 0.0488i
  0.2452 + 0.0488i







ans(:, :, 15, 3) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i
−0.0488 − 0.2452i



  0.2500
−0.2500



  0.2079 − 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.0488 − 0.2452i
  0.0488 + 0.2452i







ans(:, :, 16, 3) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.2500
−0.2500



  0.2452 − 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 1, 4) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2079 + 0.1389i
  0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 + 0.2452i
  0.0488 − 0.2452i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1389 + 0.2079i
  0.1389 − 0.2079i







ans(:, :, 2, 4) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 + 0.2079i
  0.1389 − 0.2079i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.2452 − 0.0488i
  0.2452 + 0.0488i







ans(:, :, 3, 4) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.2452 + 0.0488i
−0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 + 0.1389i
  0.2079 − 0.1389i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.0488 − 0.2452i
  0.0488 + 0.2452i







ans(:, :, 4, 4) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



−0.1389 − 0.2079i
−0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 + 0.0488i
  0.2452 − 0.0488i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 5, 4) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1389 − 0.2079i
  0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.2079 + 0.1389i
−0.2079 − 0.1389i







ans(:, :, 6, 4) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 − 0.1389i
  0.2079 + 0.1389i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.0488 + 0.2452i
  0.0488 − 0.2452i







ans(:, :, 7, 4) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.0488 + 0.2452i
  0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 − 0.2079i
  0.1389 + 0.2079i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2452 + 0.0488i
  0.2452 − 0.0488i







ans(:, :, 8, 4) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i
−0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 − 0.2452i
  0.0488 + 0.2452i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1389 − 0.2079i
  0.1389 + 0.2079i







ans(:, :, 9, 4) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i
−0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 10, 4) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 11, 4) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2452 − 0.0488i
  0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 − 0.1389i
−0.2079 + 0.1389i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 12, 4) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1389 + 0.2079i
  0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 − 0.0488i
−0.2452 + 0.0488i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.2079 + 0.1389i
  0.2079 − 0.1389i







ans(:, :, 13, 4) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.1389 + 0.2079i
−0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.2079 − 0.1389i
  0.2079 + 0.1389i







ans(:, :, 14, 4) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 + 0.1389i
−0.2079 − 0.1389i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 15, 4) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i
−0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 + 0.2079i
−0.1389 − 0.2079i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 16, 4) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2079 − 0.1389i
  0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 + 0.2452i
−0.0488 − 0.2452i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 1, 5) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.2500
−0.2500



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 2, 5) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2500
−0.2500



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 3, 5) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.2500
−0.2500



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2310 − 0.0957i
  0.2310 + 0.0957i







ans(:, :, 4, 5) =










  0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.2500
−0.2500



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 5, 5) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2500
−0.2500



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 6, 5) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.2500
−0.2500



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 7, 5) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2500
−0.2500



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 + 0.2310i
  0.0957 − 0.2310i







ans(:, :, 8, 5) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500
−0.2500



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 9, 5) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2500
−0.2500



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.0957 − 0.2310i
  0.0957 + 0.2310i







ans(:, :, 10, 5) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.2500
−0.2500



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 11, 5) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2500
−0.2500



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



  0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 12, 5) =










  0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.2500
−0.2500



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.0000 + 0.2500i
−0.0000 − 0.2500i







ans(:, :, 13, 5) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.2500
−0.2500



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



−0.2310 + 0.0957i
  0.2310 − 0.0957i







ans(:, :, 14, 5) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2500
−0.2500



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 15, 5) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.2500
−0.2500



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



  0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 16, 5) =










  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
−0.2500



  0.2500
−0.2500



  0.2500
−0.2500



  0.2500
−0.2500







ans(:, :, 1, 6) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2310 + 0.0957i
  0.2310 − 0.0957i







ans(:, :, 2, 6) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 3, 6) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 4, 6) =










  0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i







ans(:, :, 5, 6) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



  0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 6, 6) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 7, 6) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.2310 − 0.0957i
  0.2310 + 0.0957i







ans(:, :, 8, 6) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



     0 + 0.2500i
     0 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 9, 6) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



  0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 10, 6) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 11, 6) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



−0.0957 + 0.2310i
  0.0957 − 0.2310i







ans(:, :, 12, 6) =










  0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



     0 + 0.2500i
     0 − 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 13, 6) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 − 0.2310i
  0.0957 + 0.2310i







ans(:, :, 14, 6) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



  0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 15, 6) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 16, 6) =










  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



  0.2500
  0.2500



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i







ans(:, :, 1, 7) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.0488 + 0.2452i



  0.2500
−0.2500



  0.2079 + 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.0488 + 0.2452i
  0.0488 − 0.2452i







ans(:, :, 2, 7) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2500
−0.2500



  0.1389 + 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.2452 + 0.0488i
  0.2452 − 0.0488i







ans(:, :, 3, 7) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



−0.1389 − 0.2079i
−0.1389 − 0.2079i



  0.2500
−0.2500



  0.0488 + 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.1389 − 0.2079i
  0.1389 + 0.2079i







ans(:, :, 4, 7) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1389 − 0.2079i
  0.1389 − 0.2079i



  0.2500
−0.2500



−0.0488 + 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 5, 7) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2500
−0.2500



−0.1389 + 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 6, 7) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.0488 + 0.2452i
  0.0488 + 0.2452i



  0.2500
−0.2500



−0.2079 + 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 7, 7) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.2500
−0.2500



−0.2452 + 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.2079 + 0.1389i
  0.2079 − 0.1389i







ans(:, :, 8, 7) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.2500
−0.2500



−0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2079 − 0.1389i
  0.2079 + 0.1389i







ans(:, :, 9, 7) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.0488 − 0.2452i



  0.2500
−0.2500



−0.2079 − 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 10, 7) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2500
−0.2500



−0.1389 − 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 11, 7) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1389 + 0.2079i
  0.1389 + 0.2079i



  0.2500
−0.2500



−0.0488 − 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 12, 7) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.1389 + 0.2079i
−0.1389 + 0.2079i



  0.2500
−0.2500



  0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.1389 + 0.2079i
  0.1389 − 0.2079i







ans(:, :, 13, 7) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2500
−0.2500



  0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.2452 − 0.0488i
  0.2452 + 0.0488i







ans(:, :, 14, 7) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i
−0.0488 − 0.2452i



  0.2500
−0.2500



  0.2079 − 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.0488 − 0.2452i
  0.0488 + 0.2452i







ans(:, :, 15, 7) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.2500
−0.2500



  0.2452 − 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 16, 7) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.2500
−0.2500



  0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.2079 + 0.1389i
−0.2079 − 0.1389i







ans(:, :, 1, 8) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.2079 + 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 + 0.2079i
  0.1389 − 0.2079i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



−0.2452 − 0.0488i
  0.2452 + 0.0488i







ans(:, :, 2, 8) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.2452 + 0.0488i
−0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 + 0.1389i
  0.2079 − 0.1389i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.0488 − 0.2452i
  0.0488 + 0.2452i







ans(:, :, 3, 8) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



−0.1389 − 0.2079i
−0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 + 0.0488i
  0.2452 − 0.0488i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



  0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 4, 8) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.1389 − 0.2079i
  0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.2079 + 0.1389i
−0.2079 − 0.1389i







ans(:, :, 5, 8) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 − 0.1389i
  0.2079 + 0.1389i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.0488 + 0.2452i
  0.0488 − 0.2452i







ans(:, :, 6, 8) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2079 + 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.0488 + 0.2452i
  0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 − 0.2079i
  0.1389 + 0.2079i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2452 + 0.0488i
  0.2452 − 0.0488i







ans(:, :, 7, 8) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i
−0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 − 0.2452i
  0.0488 + 0.2452i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1389 − 0.2079i
  0.1389 + 0.2079i







ans(:, :, 8, 8) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i
−0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 9, 8) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.2079 − 0.1389i



  0.0957 + 0.2310i
  0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.2310 + 0.0957i
  0.2310 − 0.0957i



  0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 10, 8) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.2452 − 0.0488i
  0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 − 0.1389i
−0.2079 + 0.1389i



−0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 11, 8) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 + 0.0957i



  0.1389 + 0.2079i
  0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 − 0.0488i
−0.2452 + 0.0488i



−0.0957 − 0.2310i
  0.0957 + 0.2310i



−0.2079 + 0.1389i
  0.2079 − 0.1389i







ans(:, :, 12, 8) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.1389 + 0.2079i
−0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.2079 − 0.1389i
  0.2079 + 0.1389i







ans(:, :, 13, 8) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i
−0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 + 0.1389i
−0.2079 − 0.1389i



  0.2310 − 0.0957i
−0.2310 + 0.0957i



  0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 14, 8) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2079 − 0.1389i



  0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i
−0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 + 0.2079i
−0.1389 − 0.2079i



  0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 15, 8) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 − 0.0957i



  0.2079 − 0.1389i
  0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 + 0.2452i
−0.0488 − 0.2452i



  0.0957 + 0.2310i
−0.0957 − 0.2310i



  0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 16, 8) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2079 + 0.1389i
  0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 + 0.2452i
  0.0488 − 0.2452i



−0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1389 + 0.2079i
  0.1389 − 0.2079i







ans(:, :, 1, 9) =










  0.2500
  0.2500



  0.2500
  0.2452 + 0.0488i



  0.2500
  0.2310 + 0.0957i



  0.2500
  0.2079 + 0.1389i



  0.2500
−0.2500



  0.2500
−0.2452 − 0.0488i



  0.2500
−0.2310 − 0.0957i



  0.2500
−0.2079 − 0.1389i







ans(:, :, 2, 9) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2079 + 0.1389i



  0.1768 + 0.1768i
  0.0957 + 0.2310i



  0.0957 + 0.2310i
−0.0488 + 0.2452i



  0.2500
−0.2500



  0.2310 + 0.0957i
−0.2079 − 0.1389i



  0.1768 + 0.1768i
−0.0957 − 0.2310i



  0.0957 + 0.2310i
  0.0488 − 0.2452i







ans(:, :, 3, 9) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1389 + 0.2079i



  0.0000 + 0.2500i
−0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.2452 + 0.0488i



  0.2500
−0.2500



  0.1768 + 0.1768i
−0.1389 − 0.2079i



  0.0000 + 0.2500i
  0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.2452 − 0.0488i







ans(:, :, 4, 9) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0488 + 0.2452i



−0.1768 + 0.1768i
−0.2310 + 0.0957i



−0.2310 − 0.0957i
−0.1389 − 0.2079i



  0.2500
−0.2500



  0.0957 + 0.2310i
−0.0488 − 0.2452i



−0.1768 + 0.1768i
  0.2310 − 0.0957i



−0.2310 − 0.0957i
  0.1389 + 0.2079i







ans(:, :, 5, 9) =










  0.2500
  0.2500



  0.0000 + 0.2500i
−0.0488 + 0.2452i



−0.2500 + 0.0000i
−0.2310 − 0.0957i



−0.0000 − 0.2500i
  0.1389 − 0.2079i



  0.2500
−0.2500



  0.0000 + 0.2500i
  0.0488 − 0.2452i



−0.2500 + 0.0000i
  0.2310 + 0.0957i



−0.0000 − 0.2500i
−0.1389 + 0.2079i







ans(:, :, 6, 9) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.1389 + 0.2079i



−0.1768 − 0.1768i
−0.0957 − 0.2310i



  0.2310 − 0.0957i
  0.2452 + 0.0488i



  0.2500
−0.2500



−0.0957 + 0.2310i
  0.1389 − 0.2079i



−0.1768 − 0.1768i
  0.0957 + 0.2310i



  0.2310 − 0.0957i
−0.2452 − 0.0488i







ans(:, :, 7, 9) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.2079 + 0.1389i



−0.0000 − 0.2500i
  0.0957 − 0.2310i



  0.1768 + 0.1768i
  0.0488 + 0.2452i



  0.2500
−0.2500



−0.1768 + 0.1768i
  0.2079 − 0.1389i



−0.0000 − 0.2500i
−0.0957 + 0.2310i



  0.1768 + 0.1768i
−0.0488 − 0.2452i







ans(:, :, 8, 9) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2452 + 0.0488i



  0.1768 − 0.1768i
  0.2310 − 0.0957i



−0.0957 + 0.2310i
−0.2079 + 0.1389i



  0.2500
−0.2500



−0.2310 + 0.0957i
  0.2452 − 0.0488i



  0.1768 − 0.1768i
−0.2310 + 0.0957i



−0.0957 + 0.2310i
  0.2079 − 0.1389i







ans(:, :, 9, 9) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2452 − 0.0488i



  0.2500 − 0.0000i
  0.2310 + 0.0957i



−0.2500 + 0.0000i
−0.2079 − 0.1389i



  0.2500
−0.2500



−0.2500 + 0.0000i
  0.2452 + 0.0488i



  0.2500 − 0.0000i
−0.2310 − 0.0957i



−0.2500 + 0.0000i
  0.2079 + 0.1389i







ans(:, :, 10, 9) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2079 − 0.1389i



  0.1768 + 0.1768i
  0.0957 + 0.2310i



−0.0957 − 0.2310i
  0.0488 − 0.2452i



  0.2500
−0.2500



−0.2310 − 0.0957i
  0.2079 + 0.1389i



  0.1768 + 0.1768i
−0.0957 − 0.2310i



−0.0957 − 0.2310i
−0.0488 + 0.2452i







ans(:, :, 11, 9) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1389 − 0.2079i



  0.0000 + 0.2500i
−0.0957 + 0.2310i



  0.1768 − 0.1768i
  0.2452 − 0.0488i



  0.2500
−0.2500



−0.1768 − 0.1768i
  0.1389 + 0.2079i



  0.0000 + 0.2500i
  0.0957 − 0.2310i



  0.1768 − 0.1768i
−0.2452 + 0.0488i







ans(:, :, 12, 9) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0488 − 0.2452i



−0.1768 + 0.1768i
−0.2310 + 0.0957i



  0.2310 + 0.0957i
  0.1389 + 0.2079i



  0.2500
−0.2500



−0.0957 − 0.2310i
  0.0488 + 0.2452i



−0.1768 + 0.1768i
  0.2310 − 0.0957i



  0.2310 + 0.0957i
−0.1389 − 0.2079i







ans(:, :, 13, 9) =










  0.2500
  0.2500



−0.0000 − 0.2500i
  0.0488 − 0.2452i



−0.2500 + 0.0000i
−0.2310 − 0.0957i



  0.0000 + 0.2500i
−0.1389 + 0.2079i



  0.2500
−0.2500



−0.0000 − 0.2500i
−0.0488 + 0.2452i



−0.2500 + 0.0000i
  0.2310 + 0.0957i



  0.0000 + 0.2500i
  0.1389 − 0.2079i







ans(:, :, 14, 9) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.1389 − 0.2079i



−0.1768 − 0.1768i
−0.0957 − 0.2310i



−0.2310 + 0.0957i
−0.2452 − 0.0488i



  0.2500
−0.2500



  0.0957 − 0.2310i
−0.1389 + 0.2079i



−0.1768 − 0.1768i
  0.0957 + 0.2310i



−0.2310 + 0.0957i
  0.2452 + 0.0488i







ans(:, :, 15, 9) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.2079 − 0.1389i



−0.0000 − 0.2500i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.0488 − 0.2452i



  0.2500
−0.2500



  0.1768 − 0.1768i
−0.2079 + 0.1389i



−0.0000 − 0.2500i
−0.0957 + 0.2310i



−0.1768 − 0.1768i
  0.0488 + 0.2452i







ans(:, :, 16, 9) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2452 − 0.0488i



  0.1768 − 0.1768i
  0.2310 − 0.0957i



  0.0957 − 0.2310i
  0.2079 − 0.1389i



  0.2500
−0.2500



  0.2310 − 0.0957i
−0.2452 + 0.0488i



  0.1768 − 0.1768i
−0.2310 + 0.0957i



  0.0957 − 0.2310i
−0.2079 + 0.1389i







ans(:, :, 1, 10) =










  0.2500
  0.2500



  0.2500
  0.2452 + 0.0488i



  0.2500
  0.2310 + 0.0957i



  0.2500
  0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
  0.0488 − 0.2452i



     0 + 0.2500i
  0.0957 − 0.2310i



     0 + 0.2500i
  0.1389 − 0.2079i







ans(:, :, 2, 10) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.2079 + 0.1389i



  0.1768 + 0.1768i
  0.0957 + 0.2310i



  0.0957 + 0.2310i
−0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 + 0.2310i
  0.1389 − 0.2079i



−0.1768 + 0.1768i
  0.2310 − 0.0957i



−0.2310 + 0.0957i
  0.2452 + 0.0488i







ans(:, :, 3, 10) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.1389 + 0.2079i



  0.0000 + 0.2500i
−0.0957 + 0.2310i



−0.1768 + 0.1768i
−0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 + 0.1768i
  0.2079 − 0.1389i



−0.2500 + 0.0000i
  0.2310 + 0.0957i



−0.1768 − 0.1768i
  0.0488 + 0.2452i







ans(:, :, 4, 10) =










  0.2500
  0.2500



  0.0957 + 0.2310i
  0.0488 + 0.2452i



−0.1768 + 0.1768i
−0.2310 + 0.0957i



−0.2310 − 0.0957i
−0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 + 0.0957i
  0.2452 − 0.0488i



−0.1768 − 0.1768i
  0.0957 + 0.2310i



  0.0957 − 0.2310i
−0.2079 + 0.1389i







ans(:, :, 5, 10) =










  0.2500
  0.2500



  0.0000 + 0.2500i
−0.0488 + 0.2452i



−0.2500 + 0.0000i
−0.2310 − 0.0957i



−0.0000 − 0.2500i
  0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2500 + 0.0000i
  0.2452 + 0.0488i



−0.0000 − 0.2500i
−0.0957 + 0.2310i



  0.2500 − 0.0000i
−0.2079 − 0.1389i







ans(:, :, 6, 10) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.1389 + 0.2079i



−0.1768 − 0.1768i
−0.0957 − 0.2310i



  0.2310 − 0.0957i
  0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 − 0.0957i
  0.2079 + 0.1389i



  0.1768 − 0.1768i
−0.2310 + 0.0957i



  0.0957 + 0.2310i
  0.0488 − 0.2452i







ans(:, :, 7, 10) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.2079 + 0.1389i



−0.0000 − 0.2500i
  0.0957 − 0.2310i



  0.1768 + 0.1768i
  0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 − 0.1768i
  0.1389 + 0.2079i



  0.2500 − 0.0000i
−0.2310 − 0.0957i



−0.1768 + 0.1768i
  0.2452 − 0.0488i







ans(:, :, 8, 10) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2452 + 0.0488i



  0.1768 − 0.1768i
  0.2310 − 0.0957i



−0.0957 + 0.2310i
−0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 − 0.2310i
  0.0488 + 0.2452i



  0.1768 + 0.1768i
−0.0957 − 0.2310i



−0.2310 − 0.0957i
  0.1389 + 0.2079i







ans(:, :, 9, 10) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2452 − 0.0488i



  0.2500 − 0.0000i
  0.2310 + 0.0957i



−0.2500 + 0.0000i
−0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0000 − 0.2500i
−0.0488 + 0.2452i



  0.0000 + 0.2500i
  0.0957 − 0.2310i



−0.0000 − 0.2500i
−0.1389 + 0.2079i







ans(:, :, 10, 10) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.2079 − 0.1389i



  0.1768 + 0.1768i
  0.0957 + 0.2310i



−0.0957 − 0.2310i
  0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 − 0.2310i
−0.1389 + 0.2079i



−0.1768 + 0.1768i
  0.2310 − 0.0957i



  0.2310 − 0.0957i
−0.2452 − 0.0488i







ans(:, :, 11, 10) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.1389 − 0.2079i



  0.0000 + 0.2500i
−0.0957 + 0.2310i



  0.1768 − 0.1768i
  0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 − 0.1768i
−0.2079 + 0.1389i



−0.2500 + 0.0000i
  0.2310 + 0.0957i



  0.1768 + 0.1768i
−0.0488 − 0.2452i







ans(:, :, 12, 10) =










  0.2500
  0.2500



−0.0957 − 0.2310i
−0.0488 − 0.2452i



−0.1768 + 0.1768i
−0.2310 + 0.0957i



  0.2310 + 0.0957i
  0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 − 0.0957i
−0.2452 + 0.0488i



−0.1768 − 0.1768i
  0.0957 + 0.2310i



−0.0957 + 0.2310i
  0.2079 − 0.1389i







ans(:, :, 13, 10) =










  0.2500
  0.2500



−0.0000 − 0.2500i
  0.0488 − 0.2452i



−0.2500 + 0.0000i
−0.2310 − 0.0957i



  0.0000 + 0.2500i
−0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2500 − 0.0000i
−0.2452 − 0.0488i



−0.0000 − 0.2500i
−0.0957 + 0.2310i



−0.2500 + 0.0000i
  0.2079 + 0.1389i







ans(:, :, 14, 10) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.1389 − 0.2079i



−0.1768 − 0.1768i
−0.0957 − 0.2310i



−0.2310 + 0.0957i
−0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 + 0.0957i
−0.2079 − 0.1389i



  0.1768 − 0.1768i
−0.2310 + 0.0957i



−0.0957 − 0.2310i
−0.0488 + 0.2452i







ans(:, :, 15, 10) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.2079 − 0.1389i



−0.0000 − 0.2500i
  0.0957 − 0.2310i



−0.1768 − 0.1768i
−0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 + 0.1768i
−0.1389 − 0.2079i



  0.2500 − 0.0000i
−0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.2452 + 0.0488i







ans(:, :, 16, 10) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2452 − 0.0488i



  0.1768 − 0.1768i
  0.2310 − 0.0957i



  0.0957 − 0.2310i
  0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 + 0.2310i
−0.0488 − 0.2452i



  0.1768 + 0.1768i
−0.0957 − 0.2310i



  0.2310 + 0.0957i
−0.1389 − 0.2079i







ans(:, :, 1, 11) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2310 + 0.0957i



  0.2310 + 0.0957i
  0.1768 + 0.1768i



  0.2079 + 0.1389i
  0.0957 + 0.2310i



  0.2500
−0.2500



  0.2452 + 0.0488i
−0.2310 − 0.0957i



  0.2310 + 0.0957i
−0.1768 − 0.1768i



  0.2079 + 0.1389i
−0.0957 − 0.2310i







ans(:, :, 2, 11) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0000 + 0.2500i



−0.0488 + 0.2452i
−0.1768 + 0.1768i



  0.2500
−0.2500



  0.2079 + 0.1389i
−0.1768 − 0.1768i



  0.0957 + 0.2310i
−0.0000 − 0.2500i



−0.0488 + 0.2452i
  0.1768 − 0.1768i







ans(:, :, 3, 11) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.0957 + 0.2310i



−0.0957 + 0.2310i
−0.1768 + 0.1768i



−0.2452 + 0.0488i
−0.2310 − 0.0957i



  0.2500
−0.2500



  0.1389 + 0.2079i
−0.0957 − 0.2310i



−0.0957 + 0.2310i
  0.1768 − 0.1768i



−0.2452 + 0.0488i
  0.2310 + 0.0957i







ans(:, :, 4, 11) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0000 + 0.2500i



−0.2310 + 0.0957i
−0.2500 + 0.0000i



−0.1389 − 0.2079i
−0.0000 − 0.2500i



  0.2500
−0.2500



  0.0488 + 0.2452i
−0.0000 − 0.2500i



−0.2310 + 0.0957i
  0.2500 − 0.0000i



−0.1389 − 0.2079i
  0.0000 + 0.2500i







ans(:, :, 5, 11) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0957 + 0.2310i



−0.2310 − 0.0957i
−0.1768 − 0.1768i



  0.1389 − 0.2079i
  0.2310 − 0.0957i



  0.2500
−0.2500



−0.0488 + 0.2452i
  0.0957 − 0.2310i



−0.2310 − 0.0957i
  0.1768 + 0.1768i



  0.1389 − 0.2079i
−0.2310 + 0.0957i







ans(:, :, 6, 11) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0000 − 0.2500i



  0.2452 + 0.0488i
  0.1768 + 0.1768i



  0.2500
−0.2500



−0.1389 + 0.2079i
  0.1768 − 0.1768i



−0.0957 − 0.2310i
  0.0000 + 0.2500i



  0.2452 + 0.0488i
−0.1768 − 0.1768i







ans(:, :, 7, 11) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2310 + 0.0957i



  0.0957 − 0.2310i
  0.1768 − 0.1768i



  0.0488 + 0.2452i
−0.0957 + 0.2310i



  0.2500
−0.2500



−0.2079 + 0.1389i
  0.2310 − 0.0957i



  0.0957 − 0.2310i
−0.1768 + 0.1768i



  0.0488 + 0.2452i
  0.0957 − 0.2310i







ans(:, :, 8, 11) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2500 + 0.0000i



  0.2310 − 0.0957i
  0.2500 − 0.0000i



−0.2079 + 0.1389i
−0.2500 + 0.0000i



  0.2500
−0.2500



−0.2452 + 0.0488i
  0.2500 − 0.0000i



  0.2310 − 0.0957i
−0.2500 + 0.0000i



−0.2079 + 0.1389i
  0.2500 − 0.0000i







ans(:, :, 9, 11) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2310 − 0.0957i



  0.2310 + 0.0957i
  0.1768 + 0.1768i



−0.2079 − 0.1389i
−0.0957 − 0.2310i



  0.2500
−0.2500



−0.2452 − 0.0488i
  0.2310 + 0.0957i



  0.2310 + 0.0957i
−0.1768 − 0.1768i



−0.2079 − 0.1389i
  0.0957 + 0.2310i







ans(:, :, 10, 11) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.1768 − 0.1768i



  0.0957 + 0.2310i
  0.0000 + 0.2500i



  0.0488 − 0.2452i
  0.1768 − 0.1768i



  0.2500
−0.2500



−0.2079 − 0.1389i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
−0.0000 − 0.2500i



  0.0488 − 0.2452i
−0.1768 + 0.1768i







ans(:, :, 11, 11) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.0957 − 0.2310i



−0.0957 + 0.2310i
−0.1768 + 0.1768i



  0.2452 − 0.0488i
  0.2310 + 0.0957i



  0.2500
−0.2500



−0.1389 − 0.2079i
  0.0957 + 0.2310i



−0.0957 + 0.2310i
  0.1768 − 0.1768i



  0.2452 − 0.0488i
−0.2310 − 0.0957i







ans(:, :, 12, 11) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0000 − 0.2500i



−0.2310 + 0.0957i
−0.2500 + 0.0000i



  0.1389 + 0.2079i
  0.0000 + 0.2500i



  0.2500
−0.2500



−0.0488 − 0.2452i
  0.0000 + 0.2500i



−0.2310 + 0.0957i
  0.2500 − 0.0000i



  0.1389 + 0.2079i
−0.0000 − 0.2500i







ans(:, :, 13, 11) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0957 − 0.2310i



−0.2310 − 0.0957i
−0.1768 − 0.1768i



−0.1389 + 0.2079i
−0.2310 + 0.0957i



  0.2500
−0.2500



  0.0488 − 0.2452i
−0.0957 + 0.2310i



−0.2310 − 0.0957i
  0.1768 + 0.1768i



−0.1389 + 0.2079i
  0.2310 − 0.0957i







ans(:, :, 14, 11) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1768 − 0.1768i



−0.0957 − 0.2310i
−0.0000 − 0.2500i



−0.2452 − 0.0488i
−0.1768 − 0.1768i



  0.2500
−0.2500



  0.1389 − 0.2079i
−0.1768 + 0.1768i



−0.0957 − 0.2310i
  0.0000 + 0.2500i



−0.2452 − 0.0488i
  0.1768 + 0.1768i







ans(:, :, 15, 11) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2310 − 0.0957i



  0.0957 − 0.2310i
  0.1768 − 0.1768i



−0.0488 − 0.2452i
  0.0957 − 0.2310i



  0.2500
−0.2500



  0.2079 − 0.1389i
−0.2310 + 0.0957i



  0.0957 − 0.2310i
−0.1768 + 0.1768i



−0.0488 − 0.2452i
−0.0957 + 0.2310i







ans(:, :, 16, 11) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2500



  0.2310 − 0.0957i
  0.2500



  0.2079 − 0.1389i
  0.2500



  0.2500
−0.2500



  0.2452 − 0.0488i
−0.2500



  0.2310 − 0.0957i
−0.2500



  0.2079 − 0.1389i
−0.2500







ans(:, :, 1, 12) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2310 + 0.0957i



  0.2310 + 0.0957i
  0.1768 + 0.1768i



  0.2079 + 0.1389i
  0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 + 0.2452i
  0.0957 − 0.2310i



−0.0957 + 0.2310i
  0.1768 − 0.1768i



−0.1389 + 0.2079i
  0.2310 − 0.0957i







ans(:, :, 2, 12) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.1768 + 0.1768i



  0.0957 + 0.2310i
  0.0000 + 0.2500i



−0.0488 + 0.2452i
−0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 + 0.2079i
  0.1768 − 0.1768i



−0.2310 + 0.0957i
  0.2500 − 0.0000i



−0.2452 − 0.0488i
  0.1768 + 0.1768i







ans(:, :, 3, 12) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.0957 + 0.2310i



−0.0957 + 0.2310i
−0.1768 + 0.1768i



−0.2452 + 0.0488i
−0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 + 0.1389i
  0.2310 − 0.0957i



−0.2310 − 0.0957i
  0.1768 + 0.1768i



−0.0488 − 0.2452i
−0.0957 + 0.2310i







ans(:, :, 4, 12) =










  0.2500
  0.2500



  0.0488 + 0.2452i
  0.0000 + 0.2500i



−0.2310 + 0.0957i
−0.2500 + 0.0000i



−0.1389 − 0.2079i
−0.0000 − 0.2500i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 + 0.0488i
  0.2500 − 0.0000i



−0.0957 − 0.2310i
  0.0000 + 0.2500i



  0.2079 − 0.1389i
−0.2500 + 0.0000i







ans(:, :, 5, 12) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.0957 + 0.2310i



−0.2310 − 0.0957i
−0.1768 − 0.1768i



  0.1389 − 0.2079i
  0.2310 − 0.0957i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 − 0.0488i
  0.2310 + 0.0957i



  0.0957 − 0.2310i
−0.1768 + 0.1768i



  0.2079 + 0.1389i
−0.0957 − 0.2310i







ans(:, :, 6, 12) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.1768 + 0.1768i



−0.0957 − 0.2310i
−0.0000 − 0.2500i



  0.2452 + 0.0488i
  0.1768 + 0.1768i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 − 0.1389i
  0.1768 + 0.1768i



  0.2310 − 0.0957i
−0.2500 + 0.0000i



−0.0488 + 0.2452i
  0.1768 − 0.1768i







ans(:, :, 7, 12) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2310 + 0.0957i



  0.0957 − 0.2310i
  0.1768 − 0.1768i



  0.0488 + 0.2452i
−0.0957 + 0.2310i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 − 0.2079i
  0.0957 + 0.2310i



  0.2310 + 0.0957i
−0.1768 − 0.1768i



−0.2452 + 0.0488i
  0.2310 + 0.0957i







ans(:, :, 8, 12) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2500 + 0.0000i



  0.2310 − 0.0957i
  0.2500 − 0.0000i



−0.2079 + 0.1389i
−0.2500 + 0.0000i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 − 0.2452i
  0.0000 + 0.2500i



  0.0957 + 0.2310i
−0.0000 − 0.2500i



−0.1389 − 0.2079i
  0.0000 + 0.2500i







ans(:, :, 9, 12) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2310 − 0.0957i



  0.2310 + 0.0957i
  0.1768 + 0.1768i



−0.2079 − 0.1389i
−0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 − 0.2452i
−0.0957 + 0.2310i



−0.0957 + 0.2310i
  0.1768 − 0.1768i



  0.1389 − 0.2079i
−0.2310 + 0.0957i







ans(:, :, 10, 12) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.1768 − 0.1768i



  0.0957 + 0.2310i
  0.0000 + 0.2500i



  0.0488 − 0.2452i
  0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 − 0.2079i
−0.1768 + 0.1768i



−0.2310 + 0.0957i
  0.2500 − 0.0000i



  0.2452 + 0.0488i
−0.1768 − 0.1768i







ans(:, :, 11, 12) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.0957 − 0.2310i



−0.0957 + 0.2310i
−0.1768 + 0.1768i



  0.2452 − 0.0488i
  0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 − 0.1389i
−0.2310 + 0.0957i



−0.2310 − 0.0957i
  0.1768 + 0.1768i



  0.0488 + 0.2452i
  0.0957 − 0.2310i







ans(:, :, 12, 12) =










  0.2500
  0.2500



−0.0488 − 0.2452i
−0.0000 − 0.2500i



−0.2310 + 0.0957i
−0.2500 + 0.0000i



  0.1389 + 0.2079i
  0.0000 + 0.2500i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 − 0.0488i
−0.2500 + 0.0000i



−0.0957 − 0.2310i
  0.0000 + 0.2500i



−0.2079 + 0.1389i
  0.2500 − 0.0000i







ans(:, :, 13, 12) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.0957 − 0.2310i



−0.2310 − 0.0957i
−0.1768 − 0.1768i



−0.1389 + 0.2079i
−0.2310 + 0.0957i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 + 0.0488i
−0.2310 − 0.0957i



  0.0957 − 0.2310i
−0.1768 + 0.1768i



−0.2079 − 0.1389i
  0.0957 + 0.2310i







ans(:, :, 14, 12) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.1768 − 0.1768i



−0.0957 − 0.2310i
−0.0000 − 0.2500i



−0.2452 − 0.0488i
−0.1768 − 0.1768i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 + 0.1389i
−0.1768 − 0.1768i



  0.2310 − 0.0957i
−0.2500 + 0.0000i



  0.0488 − 0.2452i
−0.1768 + 0.1768i







ans(:, :, 15, 12) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2310 − 0.0957i



  0.0957 − 0.2310i
  0.1768 − 0.1768i



−0.0488 − 0.2452i
  0.0957 − 0.2310i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 + 0.2079i
−0.0957 − 0.2310i



  0.2310 + 0.0957i
−0.1768 − 0.1768i



  0.2452 − 0.0488i
−0.2310 − 0.0957i







ans(:, :, 16, 12) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2500



  0.2310 − 0.0957i
  0.2500



  0.2079 − 0.1389i
  0.2500



     0 + 0.2500i
     0 − 0.2500i



  0.0488 + 0.2452i
     0 − 0.2500i



  0.0957 + 0.2310i
     0 − 0.2500i



  0.1389 + 0.2079i
     0 − 0.2500i







ans(:, :, 1, 13) =










  0.2500
  0.2500



  0.2500
  0.2079 + 0.1389i



  0.2500
  0.0957 + 0.2310i



  0.2500
−0.0488 + 0.2452i



  0.2500
−0.2500



  0.2500
−0.2079 − 0.1389i



  0.2500
−0.0957 − 0.2310i



  0.2500
  0.0488 − 0.2452i







ans(:, :, 2, 13) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.1389 + 0.2079i



  0.1768 + 0.1768i
−0.0957 + 0.2310i



  0.0957 + 0.2310i
−0.2452 + 0.0488i



  0.2500
−0.2500



  0.2310 + 0.0957i
−0.1389 − 0.2079i



  0.1768 + 0.1768i
  0.0957 − 0.2310i



  0.0957 + 0.2310i
  0.2452 − 0.0488i







ans(:, :, 3, 13) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.0488 + 0.2452i



  0.0000 + 0.2500i
−0.2310 + 0.0957i



−0.1768 + 0.1768i
−0.1389 − 0.2079i



  0.2500
−0.2500



  0.1768 + 0.1768i
−0.0488 − 0.2452i



  0.0000 + 0.2500i
  0.2310 − 0.0957i



−0.1768 + 0.1768i
  0.1389 + 0.2079i







ans(:, :, 4, 13) =










  0.2500
  0.2500



  0.0957 + 0.2310i
−0.0488 + 0.2452i



−0.1768 + 0.1768i
−0.2310 − 0.0957i



−0.2310 − 0.0957i
  0.1389 − 0.2079i



  0.2500
−0.2500



  0.0957 + 0.2310i
  0.0488 − 0.2452i



−0.1768 + 0.1768i
  0.2310 + 0.0957i



−0.2310 − 0.0957i
−0.1389 + 0.2079i







ans(:, :, 5, 13) =










  0.2500
  0.2500



  0.0000 + 0.2500i
−0.1389 + 0.2079i



−0.2500 + 0.0000i
−0.0957 − 0.2310i



−0.0000 − 0.2500i
  0.2452 + 0.0488i



  0.2500
−0.2500



  0.0000 + 0.2500i
  0.1389 − 0.2079i



−0.2500 + 0.0000i
  0.0957 + 0.2310i



−0.0000 − 0.2500i
−0.2452 − 0.0488i







ans(:, :, 6, 13) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.2079 + 0.1389i



−0.1768 − 0.1768i
  0.0957 − 0.2310i



  0.2310 − 0.0957i
  0.0488 + 0.2452i



  0.2500
−0.2500



−0.0957 + 0.2310i
  0.2079 − 0.1389i



−0.1768 − 0.1768i
−0.0957 + 0.2310i



  0.2310 − 0.0957i
−0.0488 − 0.2452i







ans(:, :, 7, 13) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.2452 + 0.0488i



−0.0000 − 0.2500i
  0.2310 − 0.0957i



  0.1768 + 0.1768i
−0.2079 + 0.1389i



  0.2500
−0.2500



−0.1768 + 0.1768i
  0.2452 − 0.0488i



−0.0000 − 0.2500i
−0.2310 + 0.0957i



  0.1768 + 0.1768i
  0.2079 − 0.1389i







ans(:, :, 8, 13) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2452 − 0.0488i



  0.1768 − 0.1768i
  0.2310 + 0.0957i



−0.0957 + 0.2310i
−0.2079 − 0.1389i



  0.2500
−0.2500



−0.2310 + 0.0957i
  0.2452 + 0.0488i



  0.1768 − 0.1768i
−0.2310 − 0.0957i



−0.0957 + 0.2310i
  0.2079 + 0.1389i







ans(:, :, 9, 13) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2079 − 0.1389i



  0.2500 − 0.0000i
  0.0957 + 0.2310i



−0.2500 + 0.0000i
  0.0488 − 0.2452i



  0.2500
−0.2500



−0.2500 + 0.0000i
  0.2079 + 0.1389i



  0.2500 − 0.0000i
−0.0957 − 0.2310i



−0.2500 + 0.0000i
−0.0488 + 0.2452i







ans(:, :, 10, 13) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.1389 − 0.2079i



  0.1768 + 0.1768i
−0.0957 + 0.2310i



−0.0957 − 0.2310i
  0.2452 − 0.0488i



  0.2500
−0.2500



−0.2310 − 0.0957i
  0.1389 + 0.2079i



  0.1768 + 0.1768i
  0.0957 − 0.2310i



−0.0957 − 0.2310i
−0.2452 + 0.0488i







ans(:, :, 11, 13) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.0488 − 0.2452i



  0.0000 + 0.2500i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1389 + 0.2079i



  0.2500
−0.2500



−0.1768 − 0.1768i
  0.0488 + 0.2452i



  0.0000 + 0.2500i
  0.2310 − 0.0957i



  0.1768 − 0.1768i
−0.1389 − 0.2079i







ans(:, :, 12, 13) =










  0.2500
  0.2500



−0.0957 − 0.2310i
  0.0488 − 0.2452i



−0.1768 + 0.1768i
−0.2310 − 0.0957i



  0.2310 + 0.0957i
−0.1389 + 0.2079i



  0.2500
−0.2500



−0.0957 − 0.2310i
−0.0488 + 0.2452i



−0.1768 + 0.1768i
  0.2310 + 0.0957i



  0.2310 + 0.0957i
  0.1389 − 0.2079i







ans(:, :, 13, 13) =










  0.2500
  0.2500



−0.0000 − 0.2500i
  0.1389 − 0.2079i



−0.2500 + 0.0000i
−0.0957 − 0.2310i



  0.0000 + 0.2500i
−0.2452 − 0.0488i



  0.2500
−0.2500



−0.0000 − 0.2500i
−0.1389 + 0.2079i



−0.2500 + 0.0000i
  0.0957 + 0.2310i



  0.0000 + 0.2500i
  0.2452 + 0.0488i







ans(:, :, 14, 13) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.2079 − 0.1389i



−0.1768 − 0.1768i
  0.0957 − 0.2310i



−0.2310 + 0.0957i
−0.0488 − 0.2452i



  0.2500
−0.2500



  0.0957 − 0.2310i
−0.2079 + 0.1389i



−0.1768 − 0.1768i
−0.0957 + 0.2310i



−0.2310 + 0.0957i
  0.0488 + 0.2452i







ans(:, :, 15, 13) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.2452 − 0.0488i



−0.0000 − 0.2500i
  0.2310 − 0.0957i



−0.1768 − 0.1768i
  0.2079 − 0.1389i



  0.2500
−0.2500



  0.1768 − 0.1768i
−0.2452 + 0.0488i



−0.0000 − 0.2500i
−0.2310 + 0.0957i



−0.1768 − 0.1768i
−0.2079 + 0.1389i







ans(:, :, 16, 13) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2452 + 0.0488i



  0.1768 − 0.1768i
  0.2310 + 0.0957i



  0.0957 − 0.2310i
  0.2079 + 0.1389i



  0.2500
−0.2500



  0.2310 − 0.0957i
−0.2452 − 0.0488i



  0.1768 − 0.1768i
−0.2310 − 0.0957i



  0.0957 − 0.2310i
−0.2079 − 0.1389i







ans(:, :, 1, 14) =










  0.2500
  0.2500



  0.2500
  0.2079 + 0.1389i



  0.2500
  0.0957 + 0.2310i



  0.2500
−0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



     0 + 0.2500i
  0.1389 − 0.2079i



     0 + 0.2500i
  0.2310 − 0.0957i



     0 + 0.2500i
  0.2452 + 0.0488i







ans(:, :, 2, 14) =










  0.2500
  0.2500



  0.2310 + 0.0957i
  0.1389 + 0.2079i



  0.1768 + 0.1768i
−0.0957 + 0.2310i



  0.0957 + 0.2310i
−0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 + 0.2310i
  0.2079 − 0.1389i



−0.1768 + 0.1768i
  0.2310 + 0.0957i



−0.2310 + 0.0957i
  0.0488 + 0.2452i







ans(:, :, 3, 14) =










  0.2500
  0.2500



  0.1768 + 0.1768i
  0.0488 + 0.2452i



  0.0000 + 0.2500i
−0.2310 + 0.0957i



−0.1768 + 0.1768i
−0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 + 0.1768i
  0.2452 − 0.0488i



−0.2500 + 0.0000i
  0.0957 + 0.2310i



−0.1768 − 0.1768i
−0.2079 + 0.1389i







ans(:, :, 4, 14) =










  0.2500
  0.2500



  0.0957 + 0.2310i
−0.0488 + 0.2452i



−0.1768 + 0.1768i
−0.2310 − 0.0957i



−0.2310 − 0.0957i
  0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 + 0.0957i
  0.2452 + 0.0488i



−0.1768 − 0.1768i
−0.0957 + 0.2310i



  0.0957 − 0.2310i
−0.2079 − 0.1389i







ans(:, :, 5, 14) =










  0.2500
  0.2500



  0.0000 + 0.2500i
−0.1389 + 0.2079i



−0.2500 + 0.0000i
−0.0957 − 0.2310i



−0.0000 − 0.2500i
  0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2500 + 0.0000i
  0.2079 + 0.1389i



−0.0000 − 0.2500i
−0.2310 + 0.0957i



  0.2500 − 0.0000i
  0.0488 − 0.2452i







ans(:, :, 6, 14) =










  0.2500
  0.2500



−0.0957 + 0.2310i
−0.2079 + 0.1389i



−0.1768 − 0.1768i
  0.0957 − 0.2310i



  0.2310 − 0.0957i
  0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.2310 − 0.0957i
  0.1389 + 0.2079i



  0.1768 − 0.1768i
−0.2310 − 0.0957i



  0.0957 + 0.2310i
  0.2452 − 0.0488i







ans(:, :, 7, 14) =










  0.2500
  0.2500



−0.1768 + 0.1768i
−0.2452 + 0.0488i



−0.0000 − 0.2500i
  0.2310 − 0.0957i



  0.1768 + 0.1768i
−0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.1768 − 0.1768i
  0.0488 + 0.2452i



  0.2500 − 0.0000i
−0.0957 − 0.2310i



−0.1768 + 0.1768i
  0.1389 + 0.2079i







ans(:, :, 8, 14) =










  0.2500
  0.2500



−0.2310 + 0.0957i
−0.2452 − 0.0488i



  0.1768 − 0.1768i
  0.2310 + 0.0957i



−0.0957 + 0.2310i
−0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0957 − 0.2310i
−0.0488 + 0.2452i



  0.1768 + 0.1768i
  0.0957 − 0.2310i



−0.2310 − 0.0957i
−0.1389 + 0.2079i







ans(:, :, 9, 14) =










  0.2500
  0.2500



−0.2500 + 0.0000i
−0.2079 − 0.1389i



  0.2500 − 0.0000i
  0.0957 + 0.2310i



−0.2500 + 0.0000i
  0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.0000 − 0.2500i
−0.1389 + 0.2079i



  0.0000 + 0.2500i
  0.2310 − 0.0957i



−0.0000 − 0.2500i
−0.2452 − 0.0488i







ans(:, :, 10, 14) =










  0.2500
  0.2500



−0.2310 − 0.0957i
−0.1389 − 0.2079i



  0.1768 + 0.1768i
−0.0957 + 0.2310i



−0.0957 − 0.2310i
  0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 − 0.2310i
−0.2079 + 0.1389i



−0.1768 + 0.1768i
  0.2310 + 0.0957i



  0.2310 − 0.0957i
−0.0488 − 0.2452i







ans(:, :, 11, 14) =










  0.2500
  0.2500



−0.1768 − 0.1768i
−0.0488 − 0.2452i



  0.0000 + 0.2500i
−0.2310 + 0.0957i



  0.1768 − 0.1768i
  0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 − 0.1768i
−0.2452 + 0.0488i



−0.2500 + 0.0000i
  0.0957 + 0.2310i



  0.1768 + 0.1768i
  0.2079 − 0.1389i







ans(:, :, 12, 14) =










  0.2500
  0.2500



−0.0957 − 0.2310i
  0.0488 − 0.2452i



−0.1768 + 0.1768i
−0.2310 − 0.0957i



  0.2310 + 0.0957i
−0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 − 0.0957i
−0.2452 − 0.0488i



−0.1768 − 0.1768i
−0.0957 + 0.2310i



−0.0957 + 0.2310i
  0.2079 + 0.1389i







ans(:, :, 13, 14) =










  0.2500
  0.2500



−0.0000 − 0.2500i
  0.1389 − 0.2079i



−0.2500 + 0.0000i
−0.0957 − 0.2310i



  0.0000 + 0.2500i
−0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2500 − 0.0000i
−0.2079 − 0.1389i



−0.0000 − 0.2500i
−0.2310 + 0.0957i



−0.2500 + 0.0000i
−0.0488 + 0.2452i







ans(:, :, 14, 14) =










  0.2500
  0.2500



  0.0957 − 0.2310i
  0.2079 − 0.1389i



−0.1768 − 0.1768i
  0.0957 − 0.2310i



−0.2310 + 0.0957i
−0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.2310 + 0.0957i
−0.1389 − 0.2079i



  0.1768 − 0.1768i
−0.2310 − 0.0957i



−0.0957 − 0.2310i
−0.2452 + 0.0488i







ans(:, :, 15, 14) =










  0.2500
  0.2500



  0.1768 − 0.1768i
  0.2452 − 0.0488i



−0.0000 − 0.2500i
  0.2310 − 0.0957i



−0.1768 − 0.1768i
  0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.1768 + 0.1768i
−0.0488 − 0.2452i



  0.2500 − 0.0000i
−0.0957 − 0.2310i



  0.1768 − 0.1768i
−0.1389 − 0.2079i







ans(:, :, 16, 14) =










  0.2500
  0.2500



  0.2310 − 0.0957i
  0.2452 + 0.0488i



  0.1768 − 0.1768i
  0.2310 + 0.0957i



  0.0957 − 0.2310i
  0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0957 + 0.2310i
  0.0488 − 0.2452i



  0.1768 + 0.1768i
  0.0957 − 0.2310i



  0.2310 + 0.0957i
  0.1389 − 0.2079i







ans(:, :, 1, 15) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2079 + 0.1389i



  0.2310 + 0.0957i
  0.0957 + 0.2310i



  0.2079 + 0.1389i
−0.0488 + 0.2452i



  0.2500
−0.2500



  0.2452 + 0.0488i
−0.2079 − 0.1389i



  0.2310 + 0.0957i
−0.0957 − 0.2310i



  0.2079 + 0.1389i
  0.0488 − 0.2452i







ans(:, :, 2, 15) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.1389 + 0.2079i



  0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.2452 + 0.0488i



  0.2500
−0.2500



  0.2079 + 0.1389i
−0.1389 − 0.2079i



  0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.0488 + 0.2452i
  0.2452 − 0.0488i







ans(:, :, 3, 15) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.0488 + 0.2452i



−0.0957 + 0.2310i
−0.2310 + 0.0957i



−0.2452 + 0.0488i
−0.1389 − 0.2079i



  0.2500
−0.2500



  0.1389 + 0.2079i
−0.0488 − 0.2452i



−0.0957 + 0.2310i
  0.2310 − 0.0957i



−0.2452 + 0.0488i
  0.1389 + 0.2079i







ans(:, :, 4, 15) =










  0.2500
  0.2500



  0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.1389 − 0.2079i
  0.1389 − 0.2079i



  0.2500
−0.2500



  0.0488 + 0.2452i
  0.0488 − 0.2452i



−0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 5, 15) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.1389 + 0.2079i



−0.2310 − 0.0957i
−0.0957 − 0.2310i



  0.1389 − 0.2079i
  0.2452 + 0.0488i



  0.2500
−0.2500



−0.0488 + 0.2452i
  0.1389 − 0.2079i



−0.2310 − 0.0957i
  0.0957 + 0.2310i



  0.1389 − 0.2079i
−0.2452 − 0.0488i







ans(:, :, 6, 15) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.2079 + 0.1389i



−0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.0488 + 0.2452i



  0.2500
−0.2500



−0.1389 + 0.2079i
  0.2079 − 0.1389i



−0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.2452 + 0.0488i
−0.0488 − 0.2452i







ans(:, :, 7, 15) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2452 + 0.0488i



  0.0957 − 0.2310i
  0.2310 − 0.0957i



  0.0488 + 0.2452i
−0.2079 + 0.1389i



  0.2500
−0.2500



−0.2079 + 0.1389i
  0.2452 − 0.0488i



  0.0957 − 0.2310i
−0.2310 + 0.0957i



  0.0488 + 0.2452i
  0.2079 − 0.1389i







ans(:, :, 8, 15) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.2079 + 0.1389i
−0.2079 − 0.1389i



  0.2500
−0.2500



−0.2452 + 0.0488i
  0.2452 + 0.0488i



  0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.2079 + 0.1389i
  0.2079 + 0.1389i







ans(:, :, 9, 15) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2079 − 0.1389i



  0.2310 + 0.0957i
  0.0957 + 0.2310i



−0.2079 − 0.1389i
  0.0488 − 0.2452i



  0.2500
−0.2500



−0.2452 − 0.0488i
  0.2079 + 0.1389i



  0.2310 + 0.0957i
−0.0957 − 0.2310i



−0.2079 − 0.1389i
−0.0488 + 0.2452i







ans(:, :, 10, 15) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.1389 − 0.2079i



  0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.2452 − 0.0488i



  0.2500
−0.2500



−0.2079 − 0.1389i
  0.1389 + 0.2079i



  0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.0488 − 0.2452i
−0.2452 + 0.0488i







ans(:, :, 11, 15) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.0488 − 0.2452i



−0.0957 + 0.2310i
−0.2310 + 0.0957i



  0.2452 − 0.0488i
  0.1389 + 0.2079i



  0.2500
−0.2500



−0.1389 − 0.2079i
  0.0488 + 0.2452i



−0.0957 + 0.2310i
  0.2310 − 0.0957i



  0.2452 − 0.0488i
−0.1389 − 0.2079i







ans(:, :, 12, 15) =










  0.2500
  0.2500



−0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1389 + 0.2079i
−0.1389 + 0.2079i



  0.2500
−0.2500



−0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.1389 + 0.2079i
  0.1389 − 0.2079i







ans(:, :, 13, 15) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.1389 − 0.2079i



−0.2310 − 0.0957i
−0.0957 − 0.2310i



−0.1389 + 0.2079i
−0.2452 − 0.0488i



  0.2500
−0.2500



  0.0488 − 0.2452i
−0.1389 + 0.2079i



−0.2310 − 0.0957i
  0.0957 + 0.2310i



−0.1389 + 0.2079i
  0.2452 + 0.0488i







ans(:, :, 14, 15) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.2079 − 0.1389i



−0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.0488 − 0.2452i



  0.2500
−0.2500



  0.1389 − 0.2079i
−0.2079 + 0.1389i



−0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.2452 − 0.0488i
  0.0488 + 0.2452i







ans(:, :, 15, 15) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2452 − 0.0488i



  0.0957 − 0.2310i
  0.2310 − 0.0957i



−0.0488 − 0.2452i
  0.2079 − 0.1389i



  0.2500
−0.2500



  0.2079 − 0.1389i
−0.2452 + 0.0488i



  0.0957 − 0.2310i
−0.2310 + 0.0957i



−0.0488 − 0.2452i
−0.2079 + 0.1389i







ans(:, :, 16, 15) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.2079 − 0.1389i
  0.2079 + 0.1389i



  0.2500
−0.2500



  0.2452 − 0.0488i
−0.2452 − 0.0488i



  0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.2079 − 0.1389i
−0.2079 − 0.1389i







ans(:, :, 1, 16) =










  0.2500
  0.2500



  0.2452 + 0.0488i
  0.2079 + 0.1389i



  0.2310 + 0.0957i
  0.0957 + 0.2310i



  0.2079 + 0.1389i
−0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 + 0.2452i
  0.1389 − 0.2079i



−0.0957 + 0.2310i
  0.2310 − 0.0957i



−0.1389 + 0.2079i
  0.2452 + 0.0488i







ans(:, :, 2, 16) =










  0.2500
  0.2500



  0.2079 + 0.1389i
  0.1389 + 0.2079i



  0.0957 + 0.2310i
−0.0957 + 0.2310i



−0.0488 + 0.2452i
−0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 + 0.2079i
  0.2079 − 0.1389i



−0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2452 − 0.0488i
  0.0488 + 0.2452i







ans(:, :, 3, 16) =










  0.2500
  0.2500



  0.1389 + 0.2079i
  0.0488 + 0.2452i



−0.0957 + 0.2310i
−0.2310 + 0.0957i



−0.2452 + 0.0488i
−0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 + 0.1389i
  0.2452 − 0.0488i



−0.2310 − 0.0957i
  0.0957 + 0.2310i



−0.0488 − 0.2452i
−0.2079 + 0.1389i







ans(:, :, 4, 16) =










  0.2500
  0.2500



  0.0488 + 0.2452i
−0.0488 + 0.2452i



−0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.1389 − 0.2079i
  0.1389 − 0.2079i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 + 0.0488i
  0.2452 + 0.0488i



−0.0957 − 0.2310i
−0.0957 + 0.2310i



  0.2079 − 0.1389i
−0.2079 − 0.1389i







ans(:, :, 5, 16) =










  0.2500
  0.2500



−0.0488 + 0.2452i
−0.1389 + 0.2079i



−0.2310 − 0.0957i
−0.0957 − 0.2310i



  0.1389 − 0.2079i
  0.2452 + 0.0488i



     0 + 0.2500i
     0 − 0.2500i



−0.2452 − 0.0488i
  0.2079 + 0.1389i



  0.0957 − 0.2310i
−0.2310 + 0.0957i



  0.2079 + 0.1389i
  0.0488 − 0.2452i







ans(:, :, 6, 16) =










  0.2500
  0.2500



−0.1389 + 0.2079i
−0.2079 + 0.1389i



−0.0957 − 0.2310i
  0.0957 − 0.2310i



  0.2452 + 0.0488i
  0.0488 + 0.2452i



     0 + 0.2500i
     0 − 0.2500i



−0.2079 − 0.1389i
  0.1389 + 0.2079i



  0.2310 − 0.0957i
−0.2310 − 0.0957i



−0.0488 + 0.2452i
  0.2452 − 0.0488i







ans(:, :, 7, 16) =










  0.2500
  0.2500



−0.2079 + 0.1389i
−0.2452 + 0.0488i



  0.0957 − 0.2310i
  0.2310 − 0.0957i



  0.0488 + 0.2452i
−0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.1389 − 0.2079i
  0.0488 + 0.2452i



  0.2310 + 0.0957i
−0.0957 − 0.2310i



−0.2452 + 0.0488i
  0.1389 + 0.2079i







ans(:, :, 8, 16) =










  0.2500
  0.2500



−0.2452 + 0.0488i
−0.2452 − 0.0488i



  0.2310 − 0.0957i
  0.2310 + 0.0957i



−0.2079 + 0.1389i
−0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



−0.0488 − 0.2452i
−0.0488 + 0.2452i



  0.0957 + 0.2310i
  0.0957 − 0.2310i



−0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 9, 16) =










  0.2500
  0.2500



−0.2452 − 0.0488i
−0.2079 − 0.1389i



  0.2310 + 0.0957i
  0.0957 + 0.2310i



−0.2079 − 0.1389i
  0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 − 0.2452i
−0.1389 + 0.2079i



−0.0957 + 0.2310i
  0.2310 − 0.0957i



  0.1389 − 0.2079i
−0.2452 − 0.0488i







ans(:, :, 10, 16) =










  0.2500
  0.2500



−0.2079 − 0.1389i
−0.1389 − 0.2079i



  0.0957 + 0.2310i
−0.0957 + 0.2310i



  0.0488 − 0.2452i
  0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 − 0.2079i
−0.2079 + 0.1389i



−0.2310 + 0.0957i
  0.2310 + 0.0957i



  0.2452 + 0.0488i
−0.0488 − 0.2452i







ans(:, :, 11, 16) =










  0.2500
  0.2500



−0.1389 − 0.2079i
−0.0488 − 0.2452i



−0.0957 + 0.2310i
−0.2310 + 0.0957i



  0.2452 − 0.0488i
  0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 − 0.1389i
−0.2452 + 0.0488i



−0.2310 − 0.0957i
  0.0957 + 0.2310i



  0.0488 + 0.2452i
  0.2079 − 0.1389i







ans(:, :, 12, 16) =










  0.2500
  0.2500



−0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 + 0.0957i
−0.2310 − 0.0957i



  0.1389 + 0.2079i
−0.1389 + 0.2079i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 − 0.0488i
−0.2452 − 0.0488i



−0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.2079 + 0.1389i
  0.2079 + 0.1389i







ans(:, :, 13, 16) =










  0.2500
  0.2500



  0.0488 − 0.2452i
  0.1389 − 0.2079i



−0.2310 − 0.0957i
−0.0957 − 0.2310i



−0.1389 + 0.2079i
−0.2452 − 0.0488i



     0 + 0.2500i
     0 − 0.2500i



  0.2452 + 0.0488i
−0.2079 − 0.1389i



  0.0957 − 0.2310i
−0.2310 + 0.0957i



−0.2079 − 0.1389i
−0.0488 + 0.2452i







ans(:, :, 14, 16) =










  0.2500
  0.2500



  0.1389 − 0.2079i
  0.2079 − 0.1389i



−0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.2452 − 0.0488i
−0.0488 − 0.2452i



     0 + 0.2500i
     0 − 0.2500i



  0.2079 + 0.1389i
−0.1389 − 0.2079i



  0.2310 − 0.0957i
−0.2310 − 0.0957i



  0.0488 − 0.2452i
−0.2452 + 0.0488i







ans(:, :, 15, 16) =










  0.2500
  0.2500



  0.2079 − 0.1389i
  0.2452 − 0.0488i



  0.0957 − 0.2310i
  0.2310 − 0.0957i



−0.0488 − 0.2452i
  0.2079 − 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.1389 + 0.2079i
−0.0488 − 0.2452i



  0.2310 + 0.0957i
−0.0957 − 0.2310i



  0.2452 − 0.0488i
−0.1389 − 0.2079i







ans(:, :, 16, 16) =










  0.2500
  0.2500



  0.2452 − 0.0488i
  0.2452 + 0.0488i



  0.2310 − 0.0957i
  0.2310 + 0.0957i



  0.2079 − 0.1389i
  0.2079 + 0.1389i



     0 + 0.2500i
     0 − 0.2500i



  0.0488 + 0.2452i
  0.0488 − 0.2452i



  0.0957 + 0.2310i
  0.0957 − 0.2310i



  0.1389 + 0.2079i
  0.1389 − 0.2079i











- Rank 3





ans(:, :, 1, 1) =









  0.2041
  0.2041
  0.2041


  0.2041
  0.2041
  0.0000 + 0.2041i


  0.2041
  0.2041
−0.2041 + 0.0000i


  0.2041
  0.2041
−0.0000 − 0.2041i


  0.2041
−0.2041
−0.2041


  0.2041
−0.2041
−0.0000 − 0.2041i


  0.2041
−0.2041
  0.2041 − 0.0000i


  0.2041
−0.2041
  0.0000 + 0.2041i







ans(:, :, 2, 1) =









  0.2041
  0.2041
  0.2041


     0 + 0.2041i
     0 + 0.2041i
−0.2041 + 0.0000i


−0.2041
−0.2041
  0.2041 − 0.0000i


     0 − 0.2041i
     0 − 0.2041i
−0.2041 + 0.0000i


  0.2041
−0.2041
−0.2041


     0 + 0.2041i
     0 − 0.2041i
  0.2041 − 0.0000i


−0.2041
  0.2041
−0.2041 + 0.0000i


     0 − 0.2041i
     0 + 0.2041i
  0.2041 − 0.0000i







ans(:, :, 3, 1) =









  0.2041
  0.2041
  0.2041


−0.2041
−0.2041
−0.0000 − 0.2041i


  0.2041
  0.2041
−0.2041 + 0.0000i


−0.2041
−0.2041
  0.0000 + 0.2041i


  0.2041
−0.2041
−0.2041


−0.2041
  0.2041
  0.0000 + 0.2041i


  0.2041
−0.2041
  0.2041 − 0.0000i


−0.2041
  0.2041
−0.0000 − 0.2041i







ans(:, :, 4, 1) =









  0.2041
  0.2041
  0.2041


     0 − 0.2041i
     0 − 0.2041i
  0.2041 − 0.0000i


−0.2041
−0.2041
  0.2041 − 0.0000i


     0 + 0.2041i
     0 + 0.2041i
  0.2041 − 0.0000i


  0.2041
−0.2041
−0.2041


     0 − 0.2041i
     0 + 0.2041i
−0.2041 + 0.0000i


−0.2041
  0.2041
−0.2041 + 0.0000i


     0 + 0.2041i
     0 − 0.2041i
−0.2041 + 0.0000i







ans(:, :, 1, 2) =









  0.2041
  0.2041
  0.2041


  0.0000 + 0.2041i
  0.2041
  0.0000 + 0.2041i


−0.2041 + 0.0000i
  0.2041
−0.2041 + 0.0000i


−0.0000 − 0.2041i
  0.2041
−0.0000 − 0.2041i


  0.2041
−0.2041
−0.2041


  0.0000 + 0.2041i
−0.2041
−0.0000 − 0.2041i


−0.2041 + 0.0000i
−0.2041
  0.2041 − 0.0000i


−0.0000 − 0.2041i
−0.2041
  0.0000 + 0.2041i







ans(:, :, 2, 2) =









  0.2041
  0.2041
  0.2041


−0.2041 + 0.0000i
     0 + 0.2041i
−0.2041 + 0.0000i


  0.2041 − 0.0000i
−0.2041
  0.2041 − 0.0000i


−0.2041 + 0.0000i
     0 − 0.2041i
−0.2041 + 0.0000i


  0.2041
−0.2041
−0.2041


−0.2041 + 0.0000i
     0 − 0.2041i
  0.2041 − 0.0000i


  0.2041 − 0.0000i
  0.2041
−0.2041 + 0.0000i


−0.2041 + 0.0000i
     0 + 0.2041i
  0.2041 − 0.0000i







ans(:, :, 3, 2) =









  0.2041
  0.2041
  0.2041


−0.0000 − 0.2041i
−0.2041
−0.0000 − 0.2041i


−0.2041 + 0.0000i
  0.2041
−0.2041 + 0.0000i


  0.0000 + 0.2041i
−0.2041
  0.0000 + 0.2041i


  0.2041
−0.2041
−0.2041


−0.0000 − 0.2041i
  0.2041
  0.0000 + 0.2041i


−0.2041 + 0.0000i
−0.2041
  0.2041 − 0.0000i


  0.0000 + 0.2041i
  0.2041
−0.0000 − 0.2041i







ans(:, :, 4, 2) =









  0.2041
  0.2041
  0.2041


  0.2041 − 0.0000i
     0 − 0.2041i
  0.2041 − 0.0000i


  0.2041 − 0.0000i
−0.2041
  0.2041 − 0.0000i


  0.2041 − 0.0000i
     0 + 0.2041i
  0.2041 − 0.0000i


  0.2041
−0.2041
−0.2041


  0.2041 − 0.0000i
     0 + 0.2041i
−0.2041 + 0.0000i


  0.2041 − 0.0000i
  0.2041
−0.2041 + 0.0000i


  0.2041 − 0.0000i
     0 − 0.2041i
−0.2041 + 0.0000i







ans(:, :, 1, 3) =









  0.2041
  0.2041
  0.2041


  0.2041
  0.0000 + 0.2041i
  0.0000 + 0.2041i


  0.2041
−0.2041 + 0.0000i
−0.2041 + 0.0000i


  0.2041
−0.0000 − 0.2041i
−0.0000 − 0.2041i


  0.2041
  0.2041
−0.2041


  0.2041
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.2041
−0.2041 + 0.0000i
  0.2041 − 0.0000i


  0.2041
−0.0000 − 0.2041i
  0.0000 + 0.2041i







ans(:, :, 2, 3) =









  0.2041
  0.2041
  0.2041


     0 + 0.2041i
−0.2041 + 0.0000i
−0.2041 + 0.0000i


−0.2041
  0.2041 − 0.0000i
  0.2041 − 0.0000i


     0 − 0.2041i
−0.2041 + 0.0000i
−0.2041 + 0.0000i


  0.2041
  0.2041
−0.2041


     0 + 0.2041i
−0.2041 + 0.0000i
  0.2041 − 0.0000i


−0.2041
  0.2041 − 0.0000i
−0.2041 + 0.0000i


     0 − 0.2041i
−0.2041 + 0.0000i
  0.2041 − 0.0000i







ans(:, :, 3, 3) =









  0.2041
  0.2041
  0.2041


−0.2041
−0.0000 − 0.2041i
−0.0000 − 0.2041i


  0.2041
−0.2041 + 0.0000i
−0.2041 + 0.0000i


−0.2041
  0.0000 + 0.2041i
  0.0000 + 0.2041i


  0.2041
  0.2041
−0.2041


−0.2041
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.2041
−0.2041 + 0.0000i
  0.2041 − 0.0000i


−0.2041
  0.0000 + 0.2041i
−0.0000 − 0.2041i







ans(:, :, 4, 3) =









  0.2041
  0.2041
  0.2041


     0 − 0.2041i
  0.2041 − 0.0000i
  0.2041 − 0.0000i


−0.2041
  0.2041 − 0.0000i
  0.2041 − 0.0000i


     0 + 0.2041i
  0.2041 − 0.0000i
  0.2041 − 0.0000i


  0.2041
  0.2041
−0.2041


     0 − 0.2041i
  0.2041 − 0.0000i
−0.2041 + 0.0000i


−0.2041
  0.2041 − 0.0000i
−0.2041 + 0.0000i


     0 + 0.2041i
  0.2041 − 0.0000i
−0.2041 + 0.0000i







ans(:, :, 1, 4) =









  0.2041
  0.2041
  0.2041


  0.0000 + 0.2041i
  0.2041
  0.2041


−0.2041 + 0.0000i
  0.2041
  0.2041


−0.0000 − 0.2041i
  0.2041
  0.2041


  0.2041
  0.2041
−0.2041


  0.0000 + 0.2041i
  0.2041
−0.2041


−0.2041 + 0.0000i
  0.2041
−0.2041


−0.0000 − 0.2041i
  0.2041
−0.2041







ans(:, :, 2, 4) =









  0.2041
  0.2041
  0.2041


−0.2041 + 0.0000i
     0 + 0.2041i
     0 + 0.2041i


  0.2041 − 0.0000i
−0.2041
−0.2041


−0.2041 + 0.0000i
     0 − 0.2041i
     0 − 0.2041i


  0.2041
  0.2041
−0.2041


−0.2041 + 0.0000i
     0 + 0.2041i
     0 − 0.2041i


  0.2041 − 0.0000i
−0.2041
  0.2041


−0.2041 + 0.0000i
     0 − 0.2041i
     0 + 0.2041i







ans(:, :, 3, 4) =









  0.2041
  0.2041
  0.2041


−0.0000 − 0.2041i
−0.2041
−0.2041


−0.2041 + 0.0000i
  0.2041
  0.2041


  0.0000 + 0.2041i
−0.2041
−0.2041


  0.2041
  0.2041
−0.2041


−0.0000 − 0.2041i
−0.2041
  0.2041


−0.2041 + 0.0000i
  0.2041
−0.2041


  0.0000 + 0.2041i
−0.2041
  0.2041







ans(:, :, 4, 4) =









  0.2041
  0.2041
  0.2041


  0.2041 − 0.0000i
     0 − 0.2041i
     0 − 0.2041i


  0.2041 − 0.0000i
−0.2041
−0.2041


  0.2041 − 0.0000i
     0 + 0.2041i
     0 + 0.2041i


  0.2041
  0.2041
−0.2041


  0.2041 − 0.0000i
     0 − 0.2041i
     0 + 0.2041i


  0.2041 − 0.0000i
−0.2041
  0.2041


  0.2041 − 0.0000i
     0 + 0.2041i
     0 − 0.2041i







ans(:, :, 1, 5) =









  0.2041
  0.2041
  0.2041


  0.1886 + 0.0781i
  0.1886 + 0.0781i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.0781 + 0.1886i
  0.0781 + 0.1886i
  0.1886 − 0.0781i


  0.2041
−0.2041
−0.2041


  0.1886 + 0.0781i
−0.1886 − 0.0781i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0781 + 0.1886i
−0.0781 − 0.1886i
−0.1886 + 0.0781i







ans(:, :, 2, 5) =









  0.2041
  0.2041
  0.2041


−0.0781 + 0.1886i
−0.0781 + 0.1886i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.1886 − 0.0781i
  0.1886 − 0.0781i
−0.0781 − 0.1886i


  0.2041
−0.2041
−0.2041


−0.0781 + 0.1886i
  0.0781 − 0.1886i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.1886 − 0.0781i
−0.1886 + 0.0781i
  0.0781 + 0.1886i







ans(:, :, 3, 5) =









  0.2041
  0.2041
  0.2041


−0.1886 − 0.0781i
−0.1886 − 0.0781i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0781 − 0.1886i
−0.0781 − 0.1886i
−0.1886 + 0.0781i


  0.2041
−0.2041
−0.2041


−0.1886 − 0.0781i
  0.1886 + 0.0781i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0781 − 0.1886i
  0.0781 + 0.1886i
  0.1886 − 0.0781i







ans(:, :, 4, 5) =









  0.2041
  0.2041
  0.2041


  0.0781 − 0.1886i
  0.0781 − 0.1886i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.1886 + 0.0781i
−0.1886 + 0.0781i
  0.0781 + 0.1886i


  0.2041
−0.2041
−0.2041


  0.0781 − 0.1886i
−0.0781 + 0.1886i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.1886 + 0.0781i
  0.1886 − 0.0781i
−0.0781 − 0.1886i







ans(:, :, 1, 6) =









  0.2041
  0.2041
  0.2041


−0.0781 + 0.1886i
  0.1886 + 0.0781i
−0.0781 + 0.1886i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.1886 − 0.0781i
  0.0781 + 0.1886i
  0.1886 − 0.0781i


  0.2041
−0.2041
−0.2041


−0.0781 + 0.1886i
−0.1886 − 0.0781i
  0.0781 − 0.1886i


−0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.1886 − 0.0781i
−0.0781 − 0.1886i
−0.1886 + 0.0781i







ans(:, :, 2, 6) =









  0.2041
  0.2041
  0.2041


−0.1886 − 0.0781i
−0.0781 + 0.1886i
−0.1886 − 0.0781i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0781 − 0.1886i
  0.1886 − 0.0781i
−0.0781 − 0.1886i


  0.2041
−0.2041
−0.2041


−0.1886 − 0.0781i
  0.0781 − 0.1886i
  0.1886 + 0.0781i


  0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0781 − 0.1886i
−0.1886 + 0.0781i
  0.0781 + 0.1886i







ans(:, :, 3, 6) =









  0.2041
  0.2041
  0.2041


  0.0781 − 0.1886i
−0.1886 − 0.0781i
  0.0781 − 0.1886i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.1886 + 0.0781i
−0.0781 − 0.1886i
−0.1886 + 0.0781i


  0.2041
−0.2041
−0.2041


  0.0781 − 0.1886i
  0.1886 + 0.0781i
−0.0781 + 0.1886i


−0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.1886 + 0.0781i
  0.0781 + 0.1886i
  0.1886 − 0.0781i







ans(:, :, 4, 6) =









  0.2041
  0.2041
  0.2041


  0.1886 + 0.0781i
  0.0781 − 0.1886i
  0.1886 + 0.0781i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0781 + 0.1886i
−0.1886 + 0.0781i
  0.0781 + 0.1886i


  0.2041
−0.2041
−0.2041


  0.1886 + 0.0781i
−0.0781 + 0.1886i
−0.1886 − 0.0781i


  0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.0781 + 0.1886i
  0.1886 − 0.0781i
−0.0781 − 0.1886i







ans(:, :, 1, 7) =









  0.2041
  0.2041
  0.2041


  0.1886 + 0.0781i
−0.0781 + 0.1886i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.0781 + 0.1886i
  0.1886 − 0.0781i
  0.1886 − 0.0781i


  0.2041
  0.2041
−0.2041


  0.1886 + 0.0781i
−0.0781 + 0.1886i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0781 + 0.1886i
  0.1886 − 0.0781i
−0.1886 + 0.0781i







ans(:, :, 2, 7) =









  0.2041
  0.2041
  0.2041


−0.0781 + 0.1886i
−0.1886 − 0.0781i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.1886 − 0.0781i
−0.0781 − 0.1886i
−0.0781 − 0.1886i


  0.2041
  0.2041
−0.2041


−0.0781 + 0.1886i
−0.1886 − 0.0781i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.1886 − 0.0781i
−0.0781 − 0.1886i
  0.0781 + 0.1886i







ans(:, :, 3, 7) =









  0.2041
  0.2041
  0.2041


−0.1886 − 0.0781i
  0.0781 − 0.1886i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


−0.0781 − 0.1886i
−0.1886 + 0.0781i
−0.1886 + 0.0781i


  0.2041
  0.2041
−0.2041


−0.1886 − 0.0781i
  0.0781 − 0.1886i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0781 − 0.1886i
−0.1886 + 0.0781i
  0.1886 − 0.0781i







ans(:, :, 4, 7) =









  0.2041
  0.2041
  0.2041


  0.0781 − 0.1886i
  0.1886 + 0.0781i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


−0.1886 + 0.0781i
  0.0781 + 0.1886i
  0.0781 + 0.1886i


  0.2041
  0.2041
−0.2041


  0.0781 − 0.1886i
  0.1886 + 0.0781i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.1886 + 0.0781i
  0.0781 + 0.1886i
−0.0781 − 0.1886i







ans(:, :, 1, 8) =









  0.2041
  0.2041
  0.2041


−0.0781 + 0.1886i
  0.1886 + 0.0781i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.1886 − 0.0781i
  0.0781 + 0.1886i
  0.0781 + 0.1886i


  0.2041
  0.2041
−0.2041


−0.0781 + 0.1886i
  0.1886 + 0.0781i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.1886 − 0.0781i
  0.0781 + 0.1886i
−0.0781 − 0.1886i







ans(:, :, 2, 8) =









  0.2041
  0.2041
  0.2041


−0.1886 − 0.0781i
−0.0781 + 0.1886i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


−0.0781 − 0.1886i
  0.1886 − 0.0781i
  0.1886 − 0.0781i


  0.2041
  0.2041
−0.2041


−0.1886 − 0.0781i
−0.0781 + 0.1886i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0781 − 0.1886i
  0.1886 − 0.0781i
−0.1886 + 0.0781i







ans(:, :, 3, 8) =









  0.2041
  0.2041
  0.2041


  0.0781 − 0.1886i
−0.1886 − 0.0781i
−0.1886 − 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


−0.1886 + 0.0781i
−0.0781 − 0.1886i
−0.0781 − 0.1886i


  0.2041
  0.2041
−0.2041


  0.0781 − 0.1886i
−0.1886 − 0.0781i
  0.1886 + 0.0781i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.1886 + 0.0781i
−0.0781 − 0.1886i
  0.0781 + 0.1886i







ans(:, :, 4, 8) =









  0.2041
  0.2041
  0.2041


  0.1886 + 0.0781i
  0.0781 − 0.1886i
  0.0781 − 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.0781 + 0.1886i
−0.1886 + 0.0781i
−0.1886 + 0.0781i


  0.2041
  0.2041
−0.2041


  0.1886 + 0.0781i
  0.0781 − 0.1886i
−0.0781 + 0.1886i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0781 + 0.1886i
−0.1886 + 0.0781i
  0.1886 − 0.0781i







ans(:, :, 1, 9) =









  0.2041
  0.2041
  0.2041


  0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.2041
−0.2041
−0.2041


  0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 − 0.1443i







ans(:, :, 2, 9) =









  0.2041
  0.2041
  0.2041


−0.1443 + 0.1443i
−0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 + 0.1443i
  0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.2041
−0.2041
−0.2041


−0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 + 0.1443i







ans(:, :, 3, 9) =









  0.2041
  0.2041
  0.2041


−0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.2041
−0.2041
−0.2041


−0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 + 0.1443i







ans(:, :, 4, 9) =









  0.2041
  0.2041
  0.2041


  0.1443 − 0.1443i
  0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 − 0.1443i
−0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.2041
−0.2041
−0.2041


  0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 − 0.1443i







ans(:, :, 1, 10) =









  0.2041
  0.2041
  0.2041


−0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.2041
−0.2041
−0.2041


−0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 − 0.1443i


−0.0000 − 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 − 0.1443i







ans(:, :, 2, 10) =









  0.2041
  0.2041
  0.2041


−0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.2041
−0.2041
−0.2041


−0.1443 − 0.1443i
  0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0000 + 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 − 0.1443i
−0.1443 − 0.1443i
−0.1443 + 0.1443i







ans(:, :, 3, 10) =









  0.2041
  0.2041
  0.2041


  0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.2041
−0.2041
−0.2041


  0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 + 0.1443i


−0.0000 − 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 + 0.1443i







ans(:, :, 4, 10) =









  0.2041
  0.2041
  0.2041


  0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.2041
−0.2041
−0.2041


  0.1443 + 0.1443i
−0.1443 + 0.1443i
−0.1443 − 0.1443i


  0.0000 + 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 + 0.1443i
  0.1443 + 0.1443i
  0.1443 − 0.1443i







ans(:, :, 1, 11) =









  0.2041
  0.2041
  0.2041


  0.1443 + 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
−0.0000 − 0.2041i


−0.1443 + 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.2041
  0.2041
−0.2041


  0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i







ans(:, :, 2, 11) =









  0.2041
  0.2041
  0.2041


−0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
  0.0000 + 0.2041i


  0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.2041
  0.2041
−0.2041


−0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i







ans(:, :, 3, 11) =









  0.2041
  0.2041
  0.2041


−0.1443 − 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
−0.0000 − 0.2041i


  0.1443 − 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.2041
  0.2041
−0.2041


−0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i







ans(:, :, 4, 11) =









  0.2041
  0.2041
  0.2041


  0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
  0.0000 + 0.2041i


−0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.2041
  0.2041
−0.2041


  0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i







ans(:, :, 1, 12) =









  0.2041
  0.2041
  0.2041


−0.1443 + 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
  0.0000 + 0.2041i


  0.1443 + 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.2041
  0.2041
−0.2041


−0.1443 + 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


  0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i







ans(:, :, 2, 12) =









  0.2041
  0.2041
  0.2041


−0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
−0.0000 − 0.2041i


  0.1443 − 0.1443i
  0.1443 + 0.1443i
  0.1443 + 0.1443i


  0.2041
  0.2041
−0.2041


−0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


  0.1443 − 0.1443i
  0.1443 + 0.1443i
−0.1443 − 0.1443i







ans(:, :, 3, 12) =









  0.2041
  0.2041
  0.2041


  0.1443 − 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
  0.0000 + 0.2041i


−0.1443 − 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.2041
  0.2041
−0.2041


  0.1443 − 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i


−0.0000 − 0.2041i
  0.0000 + 0.2041i
−0.0000 − 0.2041i


−0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i







ans(:, :, 4, 12) =









  0.2041
  0.2041
  0.2041


  0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
−0.0000 − 0.2041i


−0.1443 + 0.1443i
−0.1443 − 0.1443i
−0.1443 − 0.1443i


  0.2041
  0.2041
−0.2041


  0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.0000 + 0.2041i
−0.0000 − 0.2041i
  0.0000 + 0.2041i


−0.1443 + 0.1443i
−0.1443 − 0.1443i
  0.1443 + 0.1443i







ans(:, :, 1, 13) =









  0.2041
  0.2041
  0.2041


  0.0781 + 0.1886i
  0.0781 + 0.1886i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.1886 − 0.0781i
−0.1886 − 0.0781i
−0.0781 + 0.1886i


  0.2041
−0.2041
−0.2041


  0.0781 + 0.1886i
−0.0781 − 0.1886i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.1886 − 0.0781i
  0.1886 + 0.0781i
  0.0781 − 0.1886i







ans(:, :, 2, 13) =









  0.2041
  0.2041
  0.2041


−0.1886 + 0.0781i
−0.1886 + 0.0781i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.0781 + 0.1886i
−0.0781 + 0.1886i
  0.1886 + 0.0781i


  0.2041
−0.2041
−0.2041


−0.1886 + 0.0781i
  0.1886 − 0.0781i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.0781 + 0.1886i
  0.0781 − 0.1886i
−0.1886 − 0.0781i







ans(:, :, 3, 13) =









  0.2041
  0.2041
  0.2041


−0.0781 − 0.1886i
−0.0781 − 0.1886i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.1886 + 0.0781i
  0.1886 + 0.0781i
  0.0781 − 0.1886i


  0.2041
−0.2041
−0.2041


−0.0781 − 0.1886i
  0.0781 + 0.1886i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.1886 + 0.0781i
−0.1886 − 0.0781i
−0.0781 + 0.1886i







ans(:, :, 4, 13) =









  0.2041
  0.2041
  0.2041


  0.1886 − 0.0781i
  0.1886 − 0.0781i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.0781 − 0.1886i
  0.0781 − 0.1886i
−0.1886 − 0.0781i


  0.2041
−0.2041
−0.2041


  0.1886 − 0.0781i
−0.1886 + 0.0781i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0781 − 0.1886i
−0.0781 + 0.1886i
  0.1886 + 0.0781i







ans(:, :, 1, 14) =









  0.2041
  0.2041
  0.2041


−0.1886 + 0.0781i
  0.0781 + 0.1886i
−0.1886 + 0.0781i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.0781 + 0.1886i
−0.1886 − 0.0781i
−0.0781 + 0.1886i


  0.2041
−0.2041
−0.2041


−0.1886 + 0.0781i
−0.0781 − 0.1886i
  0.1886 − 0.0781i


  0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.0781 + 0.1886i
  0.1886 + 0.0781i
  0.0781 − 0.1886i







ans(:, :, 2, 14) =









  0.2041
  0.2041
  0.2041


−0.0781 − 0.1886i
−0.1886 + 0.0781i
−0.0781 − 0.1886i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.1886 + 0.0781i
−0.0781 + 0.1886i
  0.1886 + 0.0781i


  0.2041
−0.2041
−0.2041


−0.0781 − 0.1886i
  0.1886 − 0.0781i
  0.0781 + 0.1886i


−0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.1886 + 0.0781i
  0.0781 − 0.1886i
−0.1886 − 0.0781i







ans(:, :, 3, 14) =









  0.2041
  0.2041
  0.2041


  0.1886 − 0.0781i
−0.0781 − 0.1886i
  0.1886 − 0.0781i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0781 − 0.1886i
  0.1886 + 0.0781i
  0.0781 − 0.1886i


  0.2041
−0.2041
−0.2041


  0.1886 − 0.0781i
  0.0781 + 0.1886i
−0.1886 + 0.0781i


  0.1443 − 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.0781 − 0.1886i
−0.1886 − 0.0781i
−0.0781 + 0.1886i







ans(:, :, 4, 14) =









  0.2041
  0.2041
  0.2041


  0.0781 + 0.1886i
  0.1886 − 0.0781i
  0.0781 + 0.1886i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.1886 − 0.0781i
  0.0781 − 0.1886i
−0.1886 − 0.0781i


  0.2041
−0.2041
−0.2041


  0.0781 + 0.1886i
−0.1886 + 0.0781i
−0.0781 − 0.1886i


−0.1443 + 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.1886 − 0.0781i
−0.0781 + 0.1886i
  0.1886 + 0.0781i







ans(:, :, 1, 15) =









  0.2041
  0.2041
  0.2041


  0.0781 + 0.1886i
−0.1886 + 0.0781i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


−0.1886 − 0.0781i
−0.0781 + 0.1886i
−0.0781 + 0.1886i


  0.2041
  0.2041
−0.2041


  0.0781 + 0.1886i
−0.1886 + 0.0781i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.1886 − 0.0781i
−0.0781 + 0.1886i
  0.0781 − 0.1886i







ans(:, :, 2, 15) =









  0.2041
  0.2041
  0.2041


−0.1886 + 0.0781i
−0.0781 − 0.1886i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


−0.0781 + 0.1886i
  0.1886 + 0.0781i
  0.1886 + 0.0781i


  0.2041
  0.2041
−0.2041


−0.1886 + 0.0781i
−0.0781 − 0.1886i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.0781 + 0.1886i
  0.1886 + 0.0781i
−0.1886 − 0.0781i







ans(:, :, 3, 15) =









  0.2041
  0.2041
  0.2041


−0.0781 − 0.1886i
  0.1886 − 0.0781i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.1886 + 0.0781i
  0.0781 − 0.1886i
  0.0781 − 0.1886i


  0.2041
  0.2041
−0.2041


−0.0781 − 0.1886i
  0.1886 − 0.0781i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.1886 + 0.0781i
  0.0781 − 0.1886i
−0.0781 + 0.1886i







ans(:, :, 4, 15) =









  0.2041
  0.2041
  0.2041


  0.1886 − 0.0781i
  0.0781 + 0.1886i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0781 − 0.1886i
−0.1886 − 0.0781i
−0.1886 − 0.0781i


  0.2041
  0.2041
−0.2041


  0.1886 − 0.0781i
  0.0781 + 0.1886i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0781 − 0.1886i
−0.1886 − 0.0781i
  0.1886 + 0.0781i







ans(:, :, 1, 16) =









  0.2041
  0.2041
  0.2041


−0.1886 + 0.0781i
  0.0781 + 0.1886i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


−0.0781 + 0.1886i
−0.1886 − 0.0781i
−0.1886 − 0.0781i


  0.2041
  0.2041
−0.2041


−0.1886 + 0.0781i
  0.0781 + 0.1886i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


−0.0781 + 0.1886i
−0.1886 − 0.0781i
  0.1886 + 0.0781i







ans(:, :, 2, 16) =









  0.2041
  0.2041
  0.2041


−0.0781 − 0.1886i
−0.1886 + 0.0781i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


  0.1886 + 0.0781i
−0.0781 + 0.1886i
−0.0781 + 0.1886i


  0.2041
  0.2041
−0.2041


−0.0781 − 0.1886i
−0.1886 + 0.0781i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


  0.1886 + 0.0781i
−0.0781 + 0.1886i
  0.0781 − 0.1886i







ans(:, :, 3, 16) =









  0.2041
  0.2041
  0.2041


  0.1886 − 0.0781i
−0.0781 − 0.1886i
−0.0781 − 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
−0.1443 + 0.1443i


  0.0781 − 0.1886i
  0.1886 + 0.0781i
  0.1886 + 0.0781i


  0.2041
  0.2041
−0.2041


  0.1886 − 0.0781i
−0.0781 − 0.1886i
  0.0781 + 0.1886i


  0.1443 − 0.1443i
−0.1443 + 0.1443i
  0.1443 − 0.1443i


  0.0781 − 0.1886i
  0.1886 + 0.0781i
−0.1886 − 0.0781i







ans(:, :, 4, 16) =









  0.2041
  0.2041
  0.2041


  0.0781 + 0.1886i
  0.1886 − 0.0781i
  0.1886 − 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
  0.1443 − 0.1443i


−0.1886 − 0.0781i
  0.0781 − 0.1886i
  0.0781 − 0.1886i


  0.2041
  0.2041
−0.2041


  0.0781 + 0.1886i
  0.1886 − 0.0781i
−0.1886 + 0.0781i


−0.1443 + 0.1443i
  0.1443 − 0.1443i
−0.1443 + 0.1443i


−0.1886 − 0.0781i
  0.0781 − 0.1886i
−0.0781 + 0.1886i










- Rank 4





ans(:, :, 1, 1) =


columns 1-2










  0.1768
  0.1768



  0.1768
  0.0000 + 0.1768i



  0.1768
−0.1768 + 0.0000i



  0.1768
−0.0000 − 0.1768i



  0.1768
  0.1768



  0.1768
  0.0000 + 0.1768i



  0.1768
−0.1768 + 0.0000i



  0.1768
−0.0000 − 0.1768i







columns 3-4










  0.1768
  0.1768



  0.1768
  0.0000 + 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
−0.1768



−0.1768
−0.0000 − 0.1768i



−0.1768
  0.1768 − 0.0000i



−0.1768
  0.0000 + 0.1768i







ans(:, :, 2, 1) =


columns 1-2










  0.1768
  0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i



  0.1768
  0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i







Columns 3-4










  0.1768
  0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i



−0.1768
−0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



  0.1768
−0.1768 + 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i







ans(:, :, 3, 1) =


columns 1-2










  0.1768
  0.1768



−0.1768
−0.0000 − 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
  0.0000 + 0.1768i



  0.1768
  0.1768



−0.1768
−0.0000 − 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
  0.0000 + 0.1768i







Columns 3-4










  0.1768
  0.1768



−0.1768
−0.0000 − 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
  0.0000 + 0.1768i



−0.1768
−0.1768



  0.1768
  0.0000 + 0.1768i



−0.1768
  0.1768 − 0.0000i



  0.1768
−0.0000 − 0.1768i







ans(:, :, 4, 1) =


columns 1-2










  0.1768
  0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i



  0.1768
  0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i







Columns 3-4










  0.1768
  0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i



−0.1768
−0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



  0.1768
−0.1768 + 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i







ans(:, :, 1, 2) =


  columns 1-2










  0.1768
  0.1768



  0.1768
  0.0000 + 0.1768i



  0.1768
−0.1768 + 0.0000i



  0.1768
−0.0000 − 0.1768i



     0 + 0.1768i
     0 + 0.1768i



     0 + 0.1768i
−0.1768 + 0.0000i



     0 + 0.1768i
−0.0000 − 0.1768i



     0 + 0.1768i
  0.1768 − 0.0000i







Columns 3-4










  0.1768
  0.1768



  0.1768
  0.0000 + 0.1768i



  0.1768
−0.1768 + 0.0000i



  0.1768
−0.0000 − 0.1768i



     0 − 0.1768i
     0 − 0.1768i



     0 − 0.1768i
  0.1768 − 0.0000i



     0 − 0.1768i
  0.0000 + 0.1768i



     0 − 0.1768i
−0.1768 + 0.0000i







ans(:, :, 2, 2) =


columns 1-2










  0.1768
  0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i



     0 + 0.1768i
     0 + 0.1768i



−0.1768
−0.0000 − 0.1768i



     0 − 0.1768i
  0.0000 + 0.1768i



  0.1768
−0.0000 − 0.1768i







Columns 3-4










  0.1768
  0.1768



     0 + 0.1768i
−0.1768 + 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 − 0.1768i
−0.1768 + 0.0000i



     0 − 0.1768i
     0 − 0.1768i



  0.1768
  0.0000 + 0.1768i



     0 + 0.1768i
−0.0000 − 0.1768i



−0.1768
  0.0000 + 0.1768i







ans(:, :, 3, 2) =


columns 1-2










  0.1768
  0.1768



−0.1768
−0.0000 − 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
  0.0000 + 0.1768i



     0 + 0.1768i
     0 + 0.1768i



     0 − 0.1768i
  0.1768 − 0.0000i



     0 + 0.1768i
−0.0000 − 0.1768i



     0 − 0.1768i
−0.1768 + 0.0000i







Columns 3-4










  0.1768
  0.1768



−0.1768
−0.0000 − 0.1768i



  0.1768
−0.1768 + 0.0000i



−0.1768
  0.0000 + 0.1768i



     0 − 0.1768i
     0 − 0.1768i



     0 + 0.1768i
−0.1768 + 0.0000i



     0 − 0.1768i
  0.0000 + 0.1768i



     0 + 0.1768i
  0.1768 − 0.0000i







ans(:, :, 4, 2) =


columns 1-2










  0.1768
  0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i



     0 + 0.1768i
     0 + 0.1768i



  0.1768
  0.0000 + 0.1768i



     0 − 0.1768i
  0.0000 + 0.1768i



−0.1768
  0.0000 + 0.1768i







Columns 3-4










  0.1768
  0.1768



     0 − 0.1768i
  0.1768 − 0.0000i



−0.1768
  0.1768 − 0.0000i



     0 + 0.1768i
  0.1768 − 0.0000i



     0 − 0.1768i
     0 − 0.1768i



−0.1768
−0.0000 − 0.1768i



     0 + 0.1768i
−0.0000 − 0.1768i



  0.1768
−0.0000 − 0.1768i







ans(:, :, 1, 3) =


columns 1-2










  0.1768
  0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i



  0.1768
  0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i







Columns 3-4










  0.1768
  0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i



−0.1768
−0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i







ans(:, :, 2, 3) =


columns 1-2










  0.1768
  0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i



  0.1768
  0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i







Columns 3-4










  0.1768
  0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i



−0.1768
−0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i







ans(:, :, 3, 3) =


columns 1-2










  0.1768
  0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i



  0.1768
  0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i







Columns 3-4










  0.1768
  0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i



−0.1768
−0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i







ans(:, :, 4, 3) =


columns 1-2










  0.1768
  0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i



  0.1768
  0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i







Columns 3-4










  0.1768
  0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i



−0.1768
−0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i







ans(:, :, 1, 4) =


columns 1-2










  0.1768
  0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i



     0 + 0.1768i
     0 + 0.1768i



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i







Columns 3-4










  0.1768
  0.1768



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i



     0 − 0.1768i
     0 − 0.1768i



  0.0676 − 0.1633i
  0.1633 + 0.0676i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i







ans(:, :, 2, 4) =


columns 1-2










  0.1768
  0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i



     0 + 0.1768i
     0 + 0.1768i



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i







Columns 3-4










  0.1768
  0.1768



−0.0676 + 0.1633i
−0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i



     0 − 0.1768i
     0 − 0.1768i



  0.1633 + 0.0676i
−0.0676 + 0.1633i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i







ans(:, :, 3, 4) =


columns 1-2










  0.1768
  0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i



     0 + 0.1768i
     0 + 0.1768i



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1633 − 0.0676i
−0.0676 − 0.1633i







Columns 3-4










  0.1768
  0.1768



−0.1633 − 0.0676i
  0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i



     0 − 0.1768i
     0 − 0.1768i



−0.0676 + 0.1633i
−0.1633 − 0.0676i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i







ans(:, :, 4, 4) =


Columns 1-2










  0.1768
  0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i



     0 + 0.1768i
     0 + 0.1768i



  0.1633 + 0.0676i
−0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 − 0.1633i
−0.1633 + 0.0676i







Columns 3-4










  0.1768
  0.1768



  0.0676 − 0.1633i
  0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 + 0.0676i
  0.0676 + 0.1633i



     0 − 0.1768i
     0 − 0.1768i



−0.1633 − 0.0676i
  0.0676 − 0.1633i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.0676 + 0.1633i
  0.1633 − 0.0676i







ans(:, :, 1, 5) =


Columns 1-2










  0.1768
  0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i



  0.1768
  0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i







Columns 3-4










  0.1768
  0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i



−0.1768
−0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i







ans(:, :, 2, 5) =


Columns 1-2










  0.1768
  0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1768
  0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i







Columns 3-4










  0.1768
  0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1768
−0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i







ans(:, :, 3, 5) =


Columns 1-2










  0.1768
  0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i



  0.1768
  0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i







Columns 3-4










  0.1768
  0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i



−0.1768
−0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i







ans(:, :, 4, 5) =


Columns 1-2










  0.1768
  0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.1768
  0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i







Columns 3-4










  0.1768
  0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.1768
−0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i







ans(:, :, 1, 6) =


Columns 1-2










  0.1768
  0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i



     0 + 0.1768i
     0 + 0.1768i



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.1768 + 0.0000i
  0.1768 − 0.0000i



−0.1250 − 0.1250i
−0.1250 + 0.1250i







Columns 3-4










  0.1768
  0.1768



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



−0.1250 + 0.1250i
  0.1250 + 0.1250i



     0 − 0.1768i
     0 − 0.1768i



  0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1768 − 0.0000i
−0.1768 + 0.0000i



  0.1250 + 0.1250i
  0.1250 − 0.1250i







ans(:, :, 2, 6) =


Columns 1-2










  0.1768
  0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i



     0 + 0.1768i
     0 + 0.1768i



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.1768 − 0.0000i
−0.1768 + 0.0000i



−0.1250 + 0.1250i
  0.1250 + 0.1250i







Columns 3-4










  0.1768
  0.1768



−0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



  0.1250 + 0.1250i
  0.1250 − 0.1250i



     0 − 0.1768i
     0 − 0.1768i



  0.1250 + 0.1250i
−0.1250 + 0.1250i



−0.1768 + 0.0000i
  0.1768 − 0.0000i



  0.1250 − 0.1250i
−0.1250 − 0.1250i







ans(:, :, 3, 6) =


Columns 1-2










  0.1768
  0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i



     0 + 0.1768i
     0 + 0.1768i



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1768 + 0.0000i
  0.1768 − 0.0000i



  0.1250 + 0.1250i
  0.1250 − 0.1250i







Columns 3-4










  0.1768
  0.1768



−0.1250 − 0.1250i
  0.1250 − 0.1250i



  0.0000 + 0.1768i
−0.0000 − 0.1768i



  0.1250 − 0.1250i
−0.1250 − 0.1250i



     0 − 0.1768i
     0 − 0.1768i



−0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.1768 − 0.0000i
−0.1768 + 0.0000i



−0.1250 − 0.1250i
−0.1250 + 0.1250i







ans(:, :, 4, 6) =


Columns 1-2










  0.1768
  0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i



     0 + 0.1768i
     0 + 0.1768i



  0.1250 + 0.1250i
−0.1250 + 0.1250i



  0.1768 − 0.0000i
−0.1768 + 0.0000i



  0.1250 − 0.1250i
−0.1250 − 0.1250i







Columns 3-4










  0.1768
  0.1768



  0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0000 − 0.1768i
  0.0000 + 0.1768i



−0.1250 − 0.1250i
−0.1250 + 0.1250i



     0 − 0.1768i
     0 − 0.1768i



−0.1250 − 0.1250i
  0.1250 − 0.1250i



−0.1768 + 0.0000i
  0.1768 − 0.0000i



−0.1250 + 0.1250i
  0.1250 + 0.1250i







ans(:, :, 1, 7) =


Columns 1-2










  0.1768
  0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i



  0.1768
  0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i







Columns 3-4










  0.1768
  0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i



−0.1768
−0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i







ans(:, :, 2, 7) =


Columns 1-2










  0.1768
  0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i



  0.1768
  0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i







Columns 3-4










  0.1768
  0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i



−0.1768
−0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i







ans(:, :, 3, 7) =


Columns 1-2










  0.1768
  0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i



  0.1768
  0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i







Columns 3-4










  0.1768
  0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.0676 − 0.1633i
  0.1633 − 0.0676i



  0.1633 + 0.0676i
  0.0676 − 0.1633i



−0.1768
−0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i







ans(:, :, 4, 7) =


Columns 1-2










  0.1768
  0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i



  0.1768
  0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i







Columns 3-4










  0.1768
  0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i



−0.1768
−0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i







ans(:, :, 1, 8) =


Columns 1-2










  0.1768
  0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i



     0 + 0.1768i
     0 + 0.1768i



−0.1633 + 0.0676i
−0.0676 − 0.1633i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i







Columns 3-4










  0.1768
  0.1768



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i



     0 − 0.1768i
     0 − 0.1768i



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i







ans(:, :, 2, 8) =


Columns 1-2










  0.1768
  0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i



     0 + 0.1768i
     0 + 0.1768i



−0.0676 − 0.1633i
  0.1633 − 0.0676i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i







Columns 3-4










  0.1768
  0.1768



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i



     0 − 0.1768i
     0 − 0.1768i



  0.0676 + 0.1633i
−0.1633 + 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i







ans(:, :, 3, 8) =


Columns 1-2










  0.1768
  0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i



     0 + 0.1768i
     0 + 0.1768i



  0.1633 − 0.0676i
  0.0676 + 0.1633i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.0676 + 0.1633i
  0.1633 + 0.0676i







Columns 3-4










  0.1768
  0.1768



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.1250 + 0.1250i
  0.1250 − 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i



     0 − 0.1768i
     0 − 0.1768i



−0.1633 + 0.0676i
−0.0676 − 0.1633i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i







ans(:, :, 4, 8) =


Columns 1-2










  0.1768
  0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i



     0 + 0.1768i
     0 + 0.1768i



  0.0676 + 0.1633i
−0.1633 + 0.0676i



  0.1250 + 0.1250i
−0.1250 − 0.1250i



  0.1633 + 0.0676i
  0.0676 − 0.1633i







Columns 3-4










  0.1768
  0.1768



  0.1633 − 0.0676i
  0.0676 + 0.1633i



  0.1250 − 0.1250i
−0.1250 + 0.1250i



  0.0676 − 0.1633i
−0.1633 − 0.0676i



     0 − 0.1768i
     0 − 0.1768i



−0.0676 − 0.1633i
  0.1633 − 0.0676i



−0.1250 − 0.1250i
  0.1250 + 0.1250i



−0.1633 − 0.0676i
−0.0676 + 0.1633i











- Rank 5





ans(:, :, 1) =


Colums 1-3












  0.1581
  0.1581
  0.1581


  0.1581
  0.1581
     0 + 0.1581i


  0.1581
  0.1581
−0.1581


  0.1581
  0.1581
     0 − 0.1581i


  0.1581
−0.1581
  0.1581


  0.1581
−0.1581
     0 + 0.1581i


  0.1581
−0.1581
−0.1581


  0.1581
−0.1581
     0 − 0.1581i










Colums 4-5













  0.1581
  0.1581



     0 + 0.1581i
−0.1581



−0.1581
  0.1581



     0 − 0.1581i
−0.1581



−0.1581
  0.1581



     0 − 0.1581i
−0.1581



  0.1581
  0.1581



     0 + 0.1581i
−0.1581











ans(:, :, 2) =


Colums 1-3












  0.1581
  0.1581
  0.1581


  0.1118 + 0.1118i
  0.1118 + 0.1118i
−0.1118 + 0.1118i


  0.0000 + 0.1581i
  0.0000 + 0.1581i
−0.0000 − 0.1581i


−0.1118 + 0.1118i
−0.1118 + 0.1118i
  0.1118 + 0.1118i


  0.1581
−0.1581
  0.1581


  0.1118 + 0.1118i
−0.1118 − 0.1118i
−0.1118 + 0.1118i


  0.0000 + 0.1581i
−0.0000 − 0.1581i
−0.0000 − 0.1581i


−0.1118 + 0.1118i
  0.1118 − 0.1118i
  0.1118 + 0.1118i










Colums 4-5













  0.1581
  0.1581



−0.1118 + 0.1118i
−0.1118 − 0.1118i



−0.0000 − 0.1581i
  0.0000 + 0.1581i



  0.1118 + 0.1118i
  0.1118 − 0.1118i



−0.1581
  0.1581



  0.1118 − 0.1118i
−0.1118 − 0.1118i



  0.0000 + 0.1581i
  0.0000 + 0.1581i



−0.1118 − 0.1118i
  0.1118 − 0.1118i











ans(:, :, 3) =


Colums 1-3












  0.1581
  0.1581
  0.1581


  0.1461 + 0.0605i
  0.1461 + 0.0605i
−0.0605 + 0.1461i


  0.1118 + 0.1118i
  0.1118 + 0.1118i
−0.1118 − 0.1118i


  0.0605 + 0.1461i
  0.0605 + 0.1461i
  0.1461 − 0.0605i


  0.1581
−0.1581
  0.1581


  0.1461 + 0.0605i
−0.1461 − 0.0605i
−0.0605 + 0.1461i


  0.1118 + 0.1118i
−0.1118 − 0.1118i
−0.1118 − 0.1118i


  0.0605 + 0.1461i
−0.0605 − 0.1461i
  0.1461 − 0.0605i










Colums 4-5













  0.1581
  0.1581



−0.0605 + 0.1461i
−0.1461 − 0.0605i



−0.1118 − 0.1118i
  0.1118 + 0.1118i



  0.1461 − 0.0605i
−0.0605 − 0.1461i



−0.1581
  0.1581



  0.0605 − 0.1461i
−0.1461 − 0.0605i



  0.1118 + 0.1118i
  0.1118 + 0.1118i



−0.1461 + 0.0605i
−0.0605 − 0.1461i











ans(:, :, 4) =


Colums 1-3














  0.1581
  0.1581
  0.1581
  0.1581
  0.1581


  0.0605 + 0.1461i
  0.0605 + 0.1461i
−0.1461 + 0.0605i
−0.1461 + 0.0605i
−0.0605 − 0.1461i


−0.1118 + 0.1118i
−0.1118 + 0.1118i
  0.1118 − 0.1118i


−0.1461 − 0.0605i
−0.1461 − 0.0605i
−0.0605 + 0.1461i


  0.1581
−0.1581
  0.1581


  0.0605 + 0.1461i
−0.0605 − 0.1461i
−0.1461 + 0.0605i


−0.1118 + 0.1118i
  0.1118 − 0.1118i
  0.1118 − 0.1118i


−0.1461 − 0.0605i
  0.1461 + 0.0605i
−0.0605 + 0.1461i










Colums 4-5













  0.1581
  0.1581



−0.1461 + 0.0605i
−0.0605 − 0.1461i



  0.1118 − 0.1118i
−0.1118 + 0.1118i



−0.0605 + 0.1461i
  0.1461 + 0.0605i



−0.1581
  0.1581



  0.1461 − 0.0605i
−0.0605 − 0.1461i



−0.1118 + 0.1118i
−0.1118 + 0.1118i



  0.0605 − 0.1461i
  0.1461 + 0.0605i











- Rank 6





ans(:, :, 1) =


Columns 1-3









  0.1443
  0.1443
  0.1443


  0.1443
  0.1443
     0 + 0.1443i


  0.1443
  0.1443
−0.1443


  0.1443
  0.1443
     0 − 0.1443i


  0.1443
−0.1443
  0.1443


  0.1443
−0.1443
     0 + 0.1443i


  0.1443
−0.1443
−0.1443


  0.1443
−0.1443
     0 − 0.1443i







Colums 4-6









  0.1443
  0.1443
  0.1443


     0 + 0.1443i
−0.1443
−0.1443


−0.1443
  0.1443
  0.1443


     0 − 0.1443i
−0.1443
−0.1443


−0.1443
  0.1443
−0.1443


     0 − 0.1443i
−0.1443
  0.1443


  0.1443
  0.1443
−0.1443


     0 + 0.1443i
−0.1443
  0.1443







ans(:, :, 2) =


Columns 1-3









  0.1443
  0.1443
  0.1443


  0.1021 + 0.1021i
  0.1021 + 0.1021i
−0.1021 + 0.1021i


  0.0000 + 0.1443i
  0.0000 + 0.1443i
−0.0000 − 0.1443i


−0.1021 + 0.1021i
−0.1021 + 0.1021i
  0.1021 + 0.1021i


  0.1443
−0.1443
  0.1443


  0.1021 + 0.1021i
−0.1021 − 0.1021i
−0.1021 + 0.1021i


  0.0000 + 0.1443i
−0.0000 − 0.1443i
−0.0000 − 0.1443i


−0.1021 + 0.1021i
  0.1021 − 0.1021i
  0.1021 + 0.1021i







Colums 4-6









  0.1443
  0.1443
  0.1443


−0.1021 + 0.1021i
−0.1021 − 0.1021i
−0.1021 − 0.1021i


−0.0000 − 0.1443i
  0.0000 + 0.1443i
  0.0000 + 0.1443i


  0.1021 + 0.1021i
  0.1021 − 0.1021i
  0.1021 − 0.1021i


−0.1443
  0.1443
−0.1443


  0.1021 − 0.1021i
−0.1021 − 0.1021i
  0.1021 + 0.1021i


  0.0000 + 0.1443i
  0.0000 + 0.1443i
−0.0000 − 0.1443i


−0.1021 − 0.1021i
  0.1021 − 0.1021i
−0.1021 + 0.1021i







ans(:, :, 3) =


Columns 1-3









  0.1443
  0.1443
  0.1443


  0.1334 + 0.0552i
  0.1334 + 0.0552i
−0.0552 + 0.1334i


  0.1021 + 0.1021i
  0.1021 + 0.1021i
−0.1021 − 0.1021i


  0.0552 + 0.1334i
  0.0552 + 0.1334i
  0.1334 − 0.0552i


  0.1443
−0.1443
  0.1443


  0.1334 + 0.0552i
−0.1334 − 0.0552i
−0.0552 + 0.1334i


  0.1021 + 0.1021i
−0.1021 − 0.1021i
−0.1021 − 0.1021i


  0.0552 + 0.1334i
−0.0552 − 0.1334i
  0.1334 − 0.0552i







Colums 4-6









  0.1443
  0.1443
  0.1443


−0.0552 + 0.1334i
−0.1334 − 0.0552i
−0.1334 − 0.0552i


−0.1021 − 0.1021i
  0.1021 + 0.1021i
  0.1021 + 0.1021i


  0.1334 − 0.0552i
−0.0552 − 0.1334i
−0.0552 − 0.1334i


−0.1443
  0.1443
−0.1443


  0.0552 − 0.1334i
−0.1334 − 0.0552i
  0.1334 + 0.0552i


  0.1021 + 0.1021i
  0.1021 + 0.1021i
−0.1021 − 0.1021i


−0.1334 + 0.0552i
−0.0552 − 0.1334i
  0.0552 + 0.1334i







ans(:, :, 4) =


Columns 1-3









  0.1443
  0.1443
  0.1443


  0.0552 + 0.1334i
  0.0552 + 0.1334i
−0.1334 + 0.0552i


−0.1021 + 0.1021i
−0.1021 + 0.1021i
  0.1021 − 0.1021i


−0.1334 − 0.0552i
−0.1334 − 0.0552i
−0.0552 + 0.1334i


  0.1443
−0.1443
  0.1443


  0.0552 + 0.1334i
−0.0552 − 0.1334i
−0.1334 + 0.0552i


−0.1021 + 0.1021i
  0.1021 − 0.1021i
  0.1021 − 0.1021i


−0.1334 − 0.0552i
  0.1334 + 0.0552i
−0.0552 + 0.1334i







Colums 4-6









  0.1443
  0.1443
  0.1443


−0.1334 + 0.0552i
−0.0552 − 0.1334i
−0.0552 − 0.1334i


  0.1021 − 0.1021i
−0.1021 + 0.1021i
−0.1021 + 0.1021i


−0.0552 + 0.1334i
  0.1334 + 0.0552i
  0.1334 + 0.0552i


−0.1443
  0.1443
−0.1443


  0.1334 − 0.0552i
−0.0552 − 0.1334i
  0.0552 + 0.1334i


−0.1021 + 0.1021i
−0.1021 + 0.1021i
  0.1021 − 0.1021i


  0.0552 − 0.1334i
  0.1334 + 0.0552i
−0.1334 − 0.0552i










- Rank 7





ans(:, :, 1) =


Columns 1-3












  0.1336
  0.1336
  0.1336


  0.1336
  0.1336
     0 + 0.1336i


  0.1336
  0.1336
−0.1336


  0.1336
  0.1336
     0 − 0.1336i


  0.1336
−0.1336
  0.1336


  0.1336
−0.1336
     0 + 0.1336i


  0.1336
−0.1336
−0.1336


  0.1336
−0.1336
     0 − 0.1336i










Colums 4-7















  0.1336
  0.1336
  0.1336
  0.1336



     0 + 0.1336i
−0.1336
−0.1336
     0 − 0.1336i



−0.1336
  0.1336
  0.1336
−0.1336



     0 − 0.1336i
−0.1336
−0.1336
     0 + 0.1336i



−0.1336
  0.1336
−0.1336
  0.1336



     0 − 0.1336i
−0.1336
  0.1336
     0 − 0.1336i



  0.1336
  0.1336
−0.1336
−0.1336



     0 + 0.1336i
−0.1336
  0.1336
     0 + 0.1336i











ans(:, :, 2) =


Columns 1-3












  0.1336
  0.1336
  0.1336


  0.0945 + 0.0945i
  0.0945 + 0.0945i
−0.0945 + 0.0945i


  0.0000 + 0.1336i
  0.0000 + 0.1336i
−0.0000 − 0.1336i


−0.0945 + 0.0945i
−0.0945 + 0.0945i
  0.0945 + 0.0945i


  0.1336
−0.1336
  0.1336


  0.0945 + 0.0945i
−0.0945 − 0.0945i
−0.0945 + 0.0945i


  0.0000 + 0.1336i
−0.0000 − 0.1336i
−0.0000 − 0.1336i


−0.0945 + 0.0945i
  0.0945 − 0.0945i
  0.0945 + 0.0945i










Colums 4-7















  0.1336
  0.1336
  0.1336
  0.1336



−0.0945 + 0.0945i
−0.0945 − 0.0945i
−0.0945 − 0.0945i
  0.0945 − 0.0945i



−0.0000 − 0.1336i
  0.0000 + 0.1336i
  0.0000 + 0.1336i
−0.0000 − 0.1336i



  0.0945 + 0.0945i
  0.0945 − 0.0945i
  0.0945 − 0.0945i
−0.0945 − 0.0945i



−0.1336
  0.1336
−0.1336
  0.1336



  0.0945 − 0.0945i
−0.0945 − 0.0945i
  0.0945 + 0.0945i
  0.0945 − 0.0945i



  0.0000 + 0.1336i
  0.0000 + 0.1336i
−0.0000 − 0.1336i
−0.0000 − 0.1336i



−0.0945 − 0.0945i
  0.0945 − 0.0945i
−0.0945 + 0.0945i
−0.0945 − 0.0945i











ans(:, :, 3) =


Columns 1-3












  0.1336
  0.1336
  0.1336


  0.1235 + 0.0511i
  0.1235 + 0.0511i
−0.0511 + 0.1235i


  0.0945 + 0.0945i
  0.0945 + 0.0945i
−0.0945 − 0.0945i


  0.0511 + 0.1235i
  0.0511 + 0.1235i
  0.1235 − 0.0511i


  0.1336
−0.1336
  0.1336


  0.1235 + 0.0511i
−0.1235 − 0.0511i
−0.0511 + 0.1235i


  0.0945 + 0.0945i
−0.0945 − 0.0945i
−0.0945 − 0.0945i


  0.0511 + 0.1235i
−0.0511 − 0.1235i
  0.1235 − 0.0511i










Colums 4-7















  0.1336
  0.1336
  0.1336
  0.1336



−0.0511 + 0.1235i
−0.1235 − 0.0511i
−0.1235 − 0.0511i
  0.0511 − 0.1235i



−0.0945 − 0.0945i
  0.0945 + 0.0945i
  0.0945 + 0.0945i
−0.0945 − 0.0945i



  0.1235 − 0.0511i
−0.0511 − 0.1235i
−0.0511 − 0.1235i
−0.1235 + 0.0511i



−0.1336
  0.1336
−0.1336
  0.1336



  0.0511 − 0.1235i
−0.1235 − 0.0511i
  0.1235 + 0.0511i
  0.0511 − 0.1235i



  0.0945 + 0.0945i
  0.0945 + 0.0945i
−0.0945 − 0.0945i
−0.0945 − 0.0945i



−0.1235 + 0.0511i
−0.0511 − 0.1235i
  0.0511 + 0.1235i
−0.1235 + 0.0511i











ans(:, :, 4) =


Columns 1-3












  0.1336
  0.1336
  0.1336


  0.0511 + 0.1235i
  0.0511 + 0.1235i
−0.1235 + 0.0511i


−0.0945 + 0.0945i
−0.0945 + 0.0945i
  0.0945 − 0.0945i


−0.1235 − 0.0511i
−0.1235 − 0.0511i
−0.0511 + 0.1235i


  0.1336
−0.1336
  0.1336


  0.0511 + 0.1235i
−0.0511 − 0.1235i
−0.1235 + 0.0511i


−0.0945 + 0.0945i
  0.0945 − 0.0945i
  0.0945 − 0.0945i


−0.1235 − 0.0511i
  0.1235 + 0.0511i
−0.0511 + 0.1235i










Colums 4-7















  0.1336
  0.1336
  0.1336
  0.1336



−0.1235 + 0.0511i
−0.0511 − 0.1235i
−0.0511 − 0.1235i
  0.1235 − 0.0511i



  0.0945 − 0.0945i
−0.0945 + 0.0945i
−0.0945 + 0.0945i
  0.0945 − 0.0945i



−0.0511 + 0.1235i
  0.1235 + 0.0511i
  0.1235 + 0.0511i
  0.0511 − 0.1235i



−0.1336
  0.1336
−0.1336
  0.1336



  0.1235 − 0.0511i
−0.0511 − 0.1235i
  0.0511 + 0.1235i
  0.1235 − 0.0511i



−0.0945 + 0.0945i
−0.0945 + 0.0945i
  0.0945 − 0.0945i
  0.0945 − 0.0945i



  0.0511 − 0.1235i
  0.1235 + 0.0511i
−0.1235 − 0.0511i
  0.0511 − 0.1235i











- Rank 8





ans(:, :, 1) =


Columns 1-4












  0.1250
  0.1250
  0.1250
  0.1250



  0.1250
  0.1250
   0.1250i
   0.1250i



  0.1250
  0.1250
−0.1250
−0.1250



  0.1250
  0.1250
 −0.1250i
 −0.1250i



  0.1250
−0.1250
  0.1250
−0.1250



  0.1250
−0.1250
   0.1250i
 −0.1250i



  0.1250
−0.1250
−0.1250
  0.1250



  0.1250
−0.1250
 −0.1250i
   0.1250i







Columns 5-8












  0.1250
  0.1250
  0.1250
  0.1250



−0.1250
−0.1250
 −0.1250i
 −0.1250i



  0.1250
  0.1250
−0.1250
−0.1250



−0.1250
−0.1250
   0.1250i
   0.1250i



  0.1250
−0.1250
  0.1250
−0.1250



−0.1250
  0.1250
 −0.1250i
   0.1250i



  0.1250
−0.1250
−0.1250
  0.1250



−0.1250
  0.1250
   0.1250i
 −0.1250i










FIG. 4 illustrates an example of a communication method of a receiver and a transmitter that share channel information using two codebooks.
Referring to FIG. 4, the transmitter and the receiver may maintain a memory storing a first codebook C1 and a second codebook C2.
At 420, the receiver may generate a first precoding matrix indicator from the first codebook C1, and may generate a second precoding matrix indicator from the second codebook C2 based on a state of a channel formed from the transmitter to the receiver. In this example, the first precoding matrix indicator may indicate one of first codewords included in the first codebook C1, and the second precoding matrix indicator may indicate one of second codewords included in the second codebook C2. A combination of the first precoding matrix indicator and the second precoding matrix indicator may indicate a recommended precoding matrix. For example, when the first precoding matrix indicator indicates W1 and the second precoding matrix indicator indicates W2, the recommended precoding matrix W may be calculated as W1W2.
At 430, the receiver may transmit the first precoding matrix indicator and the second precoding matrix indicator to the transmitter. The receiver may further transmit channel quality information indicating the quality of the channel and a rank indicator indicating a preferred rank.
At 440, the transmitter may extract W1 from the first codebook C1, and extract W2 from the second codebook C2, based on the first precoding matrix indicator and the second precoding matrix indicator and then generate a precoding matrix W based on W1 and W2. As described above, W may correspond to a function of W1 and W2, for example, W=W1W2.
At 450, the transmitter may precode at least one data stream based on the precoding matrix W and may transmit data. The transmitter may transmit the data using a plurality of transmit antennas, for example, 2, 4, 8, and the like.
An example in which the first codebook C1 and the second codebook C2 independently exist is described. As described above, the receiver may transmit, to the transmitter, the first precoding matrix indicator indicating the first codeword W1 included in the first codebook C1 and the second precoding matrix indicator indicating the second codeword W2 included in the second codebook C2. The transmitter may extract the first codeword W1 from the first codebook C1, and extract the second codeword W2 from the second codebook C2, based on the first precoding matrix indicator and the second precoding matrix indicator and then calculate the precoding matrix W according to a predetermined function, for example, W=W1W2. The calculated precoding matrix may be used to precode a data stream.
As another example, the overall codebook C in which the first codebook C1 and the second codebook C2 are integrated may exist. That is, probable candidates of the precoding matrix W may be calculated and thereby be pre-stored as the overall codebook C. In this example, the precoding matrix candidates included in the overall codebook C may be indicated by the first precoding matrix indicator and the second precoding matrix indicator. To indicate one of the candidates included in the overall codebook C, the receiver may transmit the first precoding matrix indicator and the second precoding matrix indicator to the transmitter. The transmitter may extract one of the candidates based on the first precoding matrix indicator and the second precoding matrix. The extracted candidate may be used to precode a data stream as a precoding matrix.
Accordingly, an example in which the first codebook C1 and the second codebook C2 are stored in the transmitter and the receiver may exist. An example in which the overall codebook C instead of the first codebook C1 and the second codebook C2 is stored may exist. In the above examples, only difference lies in that the precoding matrix W is calculated by substantially using W1 and W2. Accordingly, to store the overall codebook C in the transmitter and the receiver may be understood to be substantially equivalent to store the first codebook C1 and the second codebook C2 in the transmitter and the receiver.
Reporting Modes
As described above, the receiver may feed back, to the transmitter, a rank indicator, a first precoding matrix indicator, a second precoding matrix indicator, channel quality information (CQI), and the like. Hereinafter, a variety of reporting modes will be introduced.
1. PUCCH 1-1 Sub-Mode 2
In PUCCH 1-1 sub-mode 2, the receiver may feed back, to the transmitter via a physical uplink control channel (PUCCH), a rank indicator, a first precoding matrix indicator extracted from a subset of a first codebook C1, a second precoding matrix indicator extracted from a subset of a second codebook C2, CQI, and the like. That is, the receiver may use a previously fed back rank indicator as a presumption. CQI corresponds to CQI_s and denotes subband CQI.
For each rank, the subset of the first codebook C1 and the subset of the second codebook C2 may guarantee the whole payload size for the first precoding matrix indicator, the second precoding matrix indicator, and CQI(s) to be used within maximum N bits, for example, 11 bits.
For each rank, the subset of the first codebook C1 and the subset of the second codebook C2 may be fixed.
For each rank the subset of the first codebook C1 and the subset of the second codebook C2 may be independently present or may be integrated and thereby be present.
2. PUCCH 1-1 Sub-Mode 1
In PUCCH 1-1 sub-mode 1, the first precoding matrix indicator and the rank indicator may be fed back from the receiver to the transmitter in the same subframe.
To determine the subset of the first codebook C1 and the subset of the second codebook C2 from the first codebook C1 and the second codebook C2 may be performed dependent on a final codebook design. In particular, it may be performed to guarantee that the whole payload size may sufficiently decrease.
A recommended precoding matrix may be indicated in two subframes based on the previously fed back rank indicator.
In one subframe, the rank indicator and the first precoding matrix indicator extracted from the subset of the first codebook C1 may be commonly encoded and be fed back from the receiver to the transmitter.
In another subframe, wideband CQI and the second precoding matrix indicator extracted from the subset of the second codebook C2 may be fed back from the receiver to the transmitter. When the subset of the second codebook C2 includes only a single element, the second precoding matrix indicator may not be fed back.
3. PUCCH 2-1 Sub-Mode 1
In PUCCH 2-1 sub-mode 1, a recommended precoding matrix may be indicated in three subframes based on the previously fed back rank indicator.
In one subframe, the rank indicator and a one-bit precoder type indicator (PTI) may be fed back from the receiver to the transmitter. The PTI may have a single bit size and information to be fed back may be determined based on a value of PTI.
In another subframe, when PTI=‘0’, the first precoding matrix indicator extracted from the subset of the first codebook C1 may be reported(*fed back. When PTI=‘1’, the second precoding matrix indicator extracted from the subset of the second codebook C2 and wideband CQI may be fed back from the receiver to the transmitter.
In still another subframe, when PTI=‘0’, wideband CQI and the second precoding matrix indicator extracted from the subset of the second codebook C2 may be fed back from the receiver to the transmitter. When PTI=‘1’, subband CQI and the second precoding matrix indicator extracted from the subset of the second codebook C2 may be fed back from the receiver to the transmitter.
When the transmitter has two and four transmit antennas, PTI may be regarded as ‘1’ and may not be separately signaled.
Codebook Subset for Ranks 1, 2, 3, and 4
1. Definition of W1(k) for rank 1 and rank 2:
Similar to the aforementioned suggestion 3, definition may be made as follows:



  
    
      B
      =
      
        [
        
          
            
              
                b
                0
              
            
            
              
                b
                1
              
            
            
              ...
            
            
              
                b
                31
              
            
          
        
        ]
      
    
    ,
    
      

    
    ⁢
    
      
        
          [
          B
          ]
        
        
          
            1
            +
            m
          
          ,
          
            1
            +
            n
          
        
      
      =
      
        e
        
          j
          ⁢
          
            
              2
              ⁢
              π
              ⁢
              
                
              
              ⁢
              mn
            
            32
          
        
      
    
    ,
    
      

    
    ⁢
    
      m
      =
      0
    
    ,
    1
    ,
    2
    ,
    3
    ,
    
      n
      =
      0
    
    ,
    1
    ,
    
      ...
      ⁢
      
        
      
      ⁢
      31
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        b
                        
                          2
                          ⁢
                          kmod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                k
                              
                              +
                              1
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                k
                              
                              +
                              2
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                k
                              
                              +
                              3
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          32
                        
                      
                    
                  
                
                ]
              
            
          
        
        
          
            
              
                
                  :
                  k
                
                =
                0
              
              ,
              1
              ,
              ...
              ⁢
              
                
              
              ,
              15
            
          
        
      
      }
    
  




  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              X
              
                (
                k
                )
              
            
          
        
      
      ]
    
  




  
    
      C
      
        1
        ,
        
          (
          
            1
            ,
            2
          
          )
        
      
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            15
            )
          
        
      
      }
    
  



In this example, [B]1°m,1+n indicates an element present in an (1+m)th row and an (1+n)th column among elements belonging to B, and bz(z=0, 1, 2, . . . , 31) corresponds to a zth column vector of the matrix B, and a mod b denotes a remainder when a is divided by b.
2. Definition of W1(k) for Rank 3 and Rank 4:
Similar to the aforementioned suggestion 3, definition may be made as follows:



  
    
      B
      =
      
        [
        
          
            
              
                b
                0
              
            
            
              
                b
                1
              
            
            
              ...
            
            
              
                b
                31
              
            
          
        
        ]
      
    
    ,
    
      

    
    ⁢
    
      
        
          [
          B
          ]
        
        
          
            1
            +
            m
          
          ,
          
            1
            +
            n
          
        
      
      =
      
        e
        
          j
          ⁢
          
            
              2
              ⁢
              π
              ⁢
              
                
              
              ⁢
              mn
            
            32
          
        
      
    
    ,
    
      

    
    ⁢
    
      m
      =
      0
    
    ,
    1
    ,
    2
    ,
    3
    ,
    
      n
      =
      0
    
    ,
    1
    ,
    
      ...
      ⁢
      
        
      
      ⁢
      15
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              
                1
                2
              
              ⁡
              
                [
                
                  
                    
                      
                        b
                        
                          4
                          ⁢
                          kmod
                          ⁢
                          
                            
                          
                          ⁢
                          16
                        
                      
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                4
                                ⁢
                                k
                              
                              +
                              1
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          16
                        
                      
                    
                    
                      ...
                    
                    
                      
                        b
                        
                          
                            (
                            
                              
                                4
                                ⁢
                                k
                              
                              +
                              3
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          16
                        
                      
                    
                  
                
                ]
              
            
          
        
        
          
            
              
                
                  :
                  k
                
                =
                0
              
              ,
              1
              ,
              2
              ,
              3
            
          
        
      
      }
    
  




  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              X
              
                (
                k
                )
              
            
          
        
      
      ]
    
  



A. Subset of First Codebook and Subset of Second Codebook for PUCCH 2-1 Sub-Mode 1:
i. For ranks 2, 3, and 4, when the subset of the first codebook includes four bits and the subset of the second codebook includes two bits:
1. For Rank 2:
Hereinafter, the subset of the first codebook may be referred to as ‘C1’ and the subset of the second codebook may be referred to as ‘C2’. The subset C2 of the second codebook may be defined as follows:



  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      1
                    
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      
        {
        
          
            (
            
              
                
                  e
                  ~
                
                1
              
              ,
              
                
                  e
                  ~
                
                1
              
            
            )
          
          ,
          
            (
            
              
                
                  e
                  ~
                
                3
              
              ,
              
                
                  e
                  ~
                
                3
              
            
            )
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        
          (
          
            
              
                e
                ~
              
              2
            
            ,
            
              
                e
                ~
              
              2
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              4
            
            ,
            
              
                e
                ~
              
              4
            
          
          )
        
      
      }
    
  



2. For Rank 3:



  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              1
            
            ,
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              2
            
            ,
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              3
            
            ,
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              4
            
            ,
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
          
          )
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              5
            
            ,
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              6
            
            ,
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              7
            
            ,
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              8
            
            ,
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
          
          )
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
            ,
            
              e
              5
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
            ,
            
              e
              6
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
            ,
            
              e
              7
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
            ,
            
              e
              8
            
          
          )
        
        ,
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              [
              
                
                  
                    
                      e
                      5
                    
                  
                  
                    
                      e
                      1
                    
                  
                
              
              ]
            
            ,
            
              e
              1
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      6
                    
                  
                  
                    
                      e
                      2
                    
                  
                
              
              ]
            
            ,
            
              e
              2
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      7
                    
                  
                  
                    
                      e
                      3
                    
                  
                
              
              ]
            
            ,
            
              e
              3
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      8
                    
                  
                  
                    
                      e
                      4
                    
                  
                
              
              ]
            
            ,
            
              e
              4
            
          
          )
        
      
      }
    
  



3. For Rank 4:



  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            
              4
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                Y
              
              
                Y
              
            
            
              
                Y
              
              
                
                  -
                  Y
                
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  1
                
              
              
                
                  e
                  5
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  3
                
              
              
                
                  e
                  7
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              
                4
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  Y
                
                
                  
                    -
                    Y
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                4
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            [
            
              
                
                  
                    e
                    1
                  
                
                
                  
                    e
                    5
                  
                
              
            
            ]
          
          ,
          
            [
            
              
                
                  
                    e
                    3
                  
                
                
                  
                    e
                    7
                  
                
              
            
            ]
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  



B. Subset of First Codebook and Subset of Second Codebook for PUCCH 1-1 Sub-Mode 2:
i. For ranks 3 and 4, when the subset of the first codebook includes a single bit and the subset of the second codebook includes three bits:
1. For Rank 3:



  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        
          
            {
            
              
                W
                1
                
                  (
                  0
                  )
                
              
              ,
              
                W
                1
                
                  (
                  2
                  )
                
              
            
            }
          
          ⁢
          
            
          
          ⁢
          or
          ⁢
          
            
          
          ⁢
          
            C
            1
          
        
        =
        
          {
          
            
              W
              1
              
                (
                1
                )
              
            
            ,
            
              W
              1
              
                (
                3
                )
              
            
          
          }
        
      
    
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          
            
              
                (
                
                  
                    e
                    1
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            1
                          
                        
                        
                          
                            e
                            5
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    2
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            2
                          
                        
                        
                          
                            e
                            6
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    3
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            3
                          
                        
                        
                          
                            e
                            7
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
              
                (
                
                  
                    e
                    4
                  
                  ,
                  
                    [
                    
                      
                        
                          
                            e
                            4
                          
                        
                        
                          
                            e
                            8
                          
                        
                      
                    
                    ]
                  
                
                )
              
              ,
            
          
        
        
          
            
              
                (
                
                  
                    [
                    
                      
                        
                          
                            e
                            1
                          
                        
                        
                          
                            e
                            5
                          
                        
                      
                    
                    ]
                  
                  ,
                  
                    e
                    5
                  
                
                )
              
              ,
              
                (
                
                  
                    [
                    
                      
                        
                          
                            e
                            2
                          
                        
                        
                          
                            e
                            6
                          
                        
                      
                    
                    ]
                  
                  ,
                  
                    e
                    6
                  
                
                )
              
              ,
              
                (
                
                  
                    [
                    
                      
                        
                          
                            e
                            3
                          
                        
                        
                          
                            e
                            7
                          
                        
                      
                    
                    ]
                  
                  ,
                  
                    e
                    7
                  
                
                )
              
              ,
              
                (
                
                  
                    [
                    
                      
                        
                          
                            e
                            4
                          
                        
                        
                          
                            e
                            8
                          
                        
                      
                    
                    ]
                  
                  ,
                  
                    e
                    8
                  
                
                )
              
            
          
        
      
      }
    
  



2. For Rank 4:



  
    
      C
      1
    
    =
    
      
        
          {
          
            
              W
              1
              
                (
                0
                )
              
            
            ,
            
              W
              1
              
                (
                2
                )
              
            
          
          }
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          C
          1
        
      
      =
      
        {
        
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
        
        }
      
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  Y
                
                
                  
                    -
                    Y
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  1
                
              
              
                
                  e
                  5
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  3
                
              
              
                
                  e
                  7
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  



ii. When the Subset of the First Codebook Includes Two Bits and the Subset of the Second Codebook Includes Two Bits:
1. For Rank 1:



  
    
      C
      1
    
    =
    
      
        
          {
          
            
              W
              1
              
                (
                2
                )
              
            
            ,
            
              W
              1
              
                (
                6
                )
              
            
            ,
            
              W
              1
              
                (
                10
                )
              
            
            ,
            
              W
              1
              
                (
                14
                )
              
            
          
          }
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          C
          1
        
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              4
              )
            
          
          ,
          
            W
            1
            
              (
              8
              )
            
          
          ,
          
            W
            1
            
              (
              12
              )
            
          
        
        }
      
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        ⁡
        
          [
          
            
              
                Y
              
            
            
              
                Y
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          
            e
            ~
          
          1
        
        ,
        
          
            e
            ~
          
          2
        
        ,
        
          
            e
            ~
          
          3
        
        ,
        
          
            e
            ~
          
          4
        
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  Y
                
              
            
            ]
          
        
        ,
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            
              e
              ~
            
            1
          
          ,
          
            
              e
              ~
            
            3
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          
            e
            ~
          
          2
        
        ,
        
          
            e
            ~
          
          4
        
      
      }
    
  



2. For Rank 2:



  
    
      C
      1
    
    =
    
      
        
          {
          
            
              W
              1
              
                (
                2
                )
              
            
            ,
            
              W
              1
              
                (
                6
                )
              
            
            ,
            
              W
              1
              
                (
                10
                )
              
            
            ,
            
              W
              1
              
                (
                14
                )
              
            
          
          }
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          C
          1
        
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              4
              )
            
          
          ,
          
            W
            1
            
              (
              8
              )
            
          
          ,
          
            W
            1
            
              (
              12
              )
            
          
        
        }
      
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              
                2
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                2
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      1
                    
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      
        {
        
          
            (
            
              
                
                  e
                  ~
                
                1
              
              ,
              
                
                  e
                  ~
                
                1
              
            
            )
          
          ,
          
            (
            
              
                
                  e
                  ~
                
                3
              
              ,
              
                
                  e
                  ~
                
                3
              
            
            )
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        
          (
          
            
              
                e
                ~
              
              2
            
            ,
            
              
                e
                ~
              
              2
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              4
            
            ,
            
              
                e
                ~
              
              4
            
          
          )
        
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            
              2
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  Y
                  1
                
              
              
                
                  Y
                  2
                
              
            
            
              
                
                  Y
                  1
                
              
              
                
                  -
                  
                    Y
                    2
                  
                
              
            
          
          ]
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              
                e
                ~
              
              1
            
            ,
            
              
                e
                ~
              
              1
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              2
            
            ,
            
              
                e
                ~
              
              2
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              3
            
            ,
            
              
                e
                ~
              
              3
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              4
            
            ,
            
              
                e
                ~
              
              4
            
          
          )
        
      
      }
    
  



3. For Rank 3:



  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
        
        }
      
    
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              1
            
            ,
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              2
            
            ,
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              3
            
            ,
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              4
            
            ,
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
          
          )
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
        
        }
      
    
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              5
            
            ,
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              6
            
            ,
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              7
            
            ,
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
          
          )
        
        ,
        
          (
          
            
              e
              8
            
            ,
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
          
          )
        
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
        
        }
      
    
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              [
              
                
                  
                    
                      e
                      1
                    
                  
                  
                    
                      e
                      5
                    
                  
                
              
              ]
            
            ,
            
              e
              5
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      2
                    
                  
                  
                    
                      e
                      6
                    
                  
                
              
              ]
            
            ,
            
              e
              6
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      3
                    
                  
                  
                    
                      e
                      7
                    
                  
                
              
              ]
            
            ,
            
              e
              7
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      4
                    
                  
                  
                    
                      e
                      8
                    
                  
                
              
              ]
            
            ,
            
              e
              8
            
          
          )
        
        ,
      
      }
    
  




  
    
      
    
    ⁢
    or
  




  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
        
        }
      
    
  




  
    
      
    
    ⁢
    
      
        
          W
          2
        
        ∈
        
          C
          2
        
      
      =
      
        {
        
          
            1
            
              
                3
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        }
      
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              [
              
                
                  
                    
                      e
                      5
                    
                  
                  
                    
                      e
                      1
                    
                  
                
              
              ]
            
            ,
            
              e
              1
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      6
                    
                  
                  
                    
                      e
                      2
                    
                  
                
              
              ]
            
            ,
            
              e
              2
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      7
                    
                  
                  
                    
                      e
                      3
                    
                  
                
              
              ]
            
            ,
            
              e
              3
            
          
          )
        
        ,
        
          (
          
            
              [
              
                
                  
                    
                      e
                      8
                    
                  
                  
                    
                      e
                      4
                    
                  
                
              
              ]
            
            ,
            
              e
              4
            
          
          )
        
      
      }
    
  



4. For Rank 4:



  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        
          W
          1
          
            (
            3
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            
              4
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                Y
              
              
                Y
              
            
            
              
                Y
              
              
                
                  -
                  Y
                
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  1
                
              
              
                
                  e
                  5
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  3
                
              
              
                
                  e
                  7
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  




  or




  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        
          W
          1
          
            (
            3
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              
                4
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  Y
                
                
                  
                    -
                    Y
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                4
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  Y
                
                
                  Y
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            [
            
              
                
                  
                    e
                    1
                  
                
                
                  
                    e
                    5
                  
                
              
            
            ]
          
          ,
          
            [
            
              
                
                  
                    e
                    3
                  
                
                
                  
                    e
                    7
                  
                
              
            
            ]
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          [
          
            
              
                
                  e
                  2
                
              
              
                
                  e
                  6
                
              
            
          
          ]
        
        ,
        
          [
          
            
              
                
                  e
                  4
                
              
              
                
                  e
                  8
                
              
            
          
          ]
        
      
      }
    
  



iii. When the Subset of the First Codebook Includes Three Bits and the Subset of the Second Codebook Includes a Single Bit:
1. For Rank 1:



  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        
          W
          1
          
            (
            4
            )
          
        
        ,
        
          W
          1
          
            (
            6
            )
          
        
        ,
        
          W
          1
          
            (
            8
            )
          
        
        ,
        
          W
          1
          
            (
            10
            )
          
        
        ,
        
          W
          1
          
            (
            12
            )
          
        
        ,
        
          W
          1
          
            (
            14
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        ⁡
        
          [
          
            
              
                Y
              
            
            
              
                Y
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          
            e
            ~
          
          1
        
        ,
        
          
            e
            ~
          
          3
        
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  Y
                
              
            
            ]
          
        
        ,
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            e
            ~
          
          1
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          2
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          3
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          e
          ~
        
        4
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  Y
                
              
            
            ]
          
        
        ,
        
          
            1
            
              2
            
          
          ⁡
          
            [
            
              
                
                  Y
                
              
              
                
                  
                    -
                    Y
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            e
            ~
          
          1
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          2
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          3
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          e
          ~
        
        4
      
      }
    
  



2. For Rank 2:



  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        
          W
          1
          
            (
            4
            )
          
        
        ,
        
          W
          1
          
            (
            6
            )
          
        
        ,
        
          W
          1
          
            (
            8
            )
          
        
        ,
        
          W
          1
          
            (
            10
            )
          
        
        ,
        
          W
          1
          
            (
            12
            )
          
        
        ,
        
          W
          1
          
            (
            14
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          
            1
            
              
                2
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    Y
                    1
                  
                
                
                  
                    -
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            1
            
              
                2
              
              ⁢
              
                2
              
            
          
          ⁡
          
            [
            
              
                
                  
                    Y
                    1
                  
                
                
                  
                    Y
                    2
                  
                
              
              
                
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      1
                    
                  
                
                
                  
                    
                      -
                      j
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      2
                    
                  
                
              
            
            ]
          
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      
        {
        
          (
          
            
              
                e
                ~
              
              1
            
            ,
            
              
                e
                ~
              
              1
            
          
          )
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        (
        
          
            
              e
              ~
            
            2
          
          ,
          
            
              e
              ~
            
            2
          
        
        )
      
      }
    
  




  
    
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      
        {
        
          (
          
            
              
                e
                ~
              
              3
            
            ,
            
              
                e
                ~
              
              3
            
          
          )
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        (
        
          
            
              e
              ~
            
            4
          
          ,
          
            
              e
              ~
            
            4
          
        
        )
      
      }
    
  




  or




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            
              2
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  Y
                  1
                
              
              
                
                  Y
                  2
                
              
            
            
              
                
                  Y
                  1
                
              
              
                
                  -
                  
                    Y
                    2
                  
                
              
            
          
          ]
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      
        {
        
          
            (
            
              
                
                  e
                  ~
                
                1
              
              ,
              
                
                  e
                  ~
                
                1
              
            
            )
          
          ,
          
            (
            
              
                
                  e
                  ~
                
                3
              
              ,
              
                
                  e
                  ~
                
                3
              
            
            )
          
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        
          (
          
            
              
                e
                ~
              
              2
            
            ,
            
              
                e
                ~
              
              2
            
          
          )
        
        ,
        
          (
          
            
              
                e
                ~
              
              4
            
            ,
            
              
                e
                ~
              
              4
            
          
          )
        
      
      }
    
  



3. For Rank 3 and Rank 4:
The subset C1 of the first codebook and the subset C2 of the second codebook for rank 3 and rank 4 may be the same as the subset C1 of the 2-bit first codebook and the subset C2 of the 2-bit second codebook that are described above. For rank 3 and rank 4, the subset C1 of the first codebook may have only a size of two bits.
iv. When the Subset of the First Codebook Includes Four Bits and the Subset of the Second Codebook Includes Zero Bit:
1. For Rank 1:



  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            15
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        ⁡
        
          [
          
            
              
                Y
              
            
            
              
                Y
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      
        {
        
          
            e
            ~
          
          1
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          2
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      
        {
        
          
            e
            ~
          
          3
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      Y
    
    ∈
    
      {
      
        
          e
          ~
        
        4
      
      }
    
  




  or




  
    
      C
      1
    
    =
    
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          
            W
            1
            
              (
              4
              )
            
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            W
            1
            
              (
              14
              )
            
          
        
        }
      
      ⁢
      
        
      
      ⁢
      with
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        ⁡
        
          [
          
            
              
                Y
              
            
            
              
                Y
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          e
          ~
        
        1
      
      }
    
  




  or




  
    
      C
      1
    
    =
    
      
        {
        
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              3
              )
            
          
          ,
          
            W
            1
            
              (
              5
              )
            
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            W
            1
            
              (
              15
              )
            
          
        
        }
      
      ⁢
      
        
      
      ⁢
      with
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        ⁡
        
          [
          
            
              
                Y
              
            
            
              
                
                  -
                  Y
                
              
            
          
          ]
        
      
      }
    
  




  
    Y
    ∈
    
      {
      
        
          e
          ~
        
        1
      
      }
    
  



2. For Rank 2:



  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        
          W
          1
          
            (
            2
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            15
            )
          
        
      
      }
    
  




  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            
              2
            
            ⁢
            
              2
            
          
        
        ⁡
        
          [
          
            
              
                
                  Y
                  1
                
              
              
                
                  Y
                  2
                
              
            
            
              
                
                  Y
                  1
                
              
              
                
                  -
                  
                    Y
                    2
                  
                
              
            
          
          ]
        
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      
        {
        
          (
          
            
              
                e
                ~
              
              1
            
            ,
            
              
                e
                ~
              
              1
            
          
          )
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        (
        
          
            
              e
              ~
            
            2
          
          ,
          
            
              e
              ~
            
            2
          
        
        )
      
      }
    
  




  
    
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      
        {
        
          (
          
            
              
                e
                ~
              
              3
            
            ,
            
              
                e
                ~
              
              3
            
          
          )
        
        }
      
      ⁢
      
        
      
      ⁢
      or
      ⁢
      
        
      
      ⁢
      
        (
        
          
            Y
            1
          
          ,
          
            Y
            2
          
        
        )
      
    
    ∈
    
      {
      
        (
        
          
            
              e
              ~
            
            4
          
          ,
          
            
              e
              ~
            
            4
          
        
        )
      
      }
    
  



3. For Rank 3 and Rank 4:
The subset C1 of the first codebook and the subset C2 of the second codebook for rank 3 and rank 4 may be the same as the subset C1 of the 2-bit first codebook and the subset C2 of the 2-bit second codebook that are described above. For rank 3 and rank 4, the subset C1 of the first codebook may have only a size of two bits.
C. Subset of First Codebook for PUCCH 1-1 Sub-Mode 1 when a Rank Indicator and a First Precoding Matrix Indicator are Commonly Encoded:
i. Five Bits of Common Encoding of Rank Indicator and First Precoding Matrix Indicator—Example 1:
1. For Rank 1 and Rank 2:

C1={W1(0),W1(2),W1(4),W1(6),W1(8),W1(10),W1(12),W1(14)}

or

C1{W1(1),W1(3),W1(5),W1(7),W1(9),W1(11),W1(13),W1(15)}

2. For Rank 3 and Rank 4:

C1={W1(1),W1(3)}

or

C1={W1(1),W1(3)}

3. For Rank 5 and Rank 6:

C1={W1(0),W1(1),W1(2),W1(3)}

4. For Rank 7:

C1={W1(0),W1(1),W1(2)}

5. For Rank 8:

C1={W1(0)}

ii. Five Bits of Common Encoding of Rank Indicator and First Precoding Matrix Indicator—Example 2:
1. For Rank 1 and Rank 2:

C1={W1(0),W1(2),W1(4),W1(6),W1(8),W1(10),W1(12),W1(14)}

or

C1={W1(1),W1(3),W1(5),W1(7),W1(9),W1(11),W1(13),W1(15)}

2. For Rank 3 and Rank 4:

C1={W1(0),W1(1),W1(2),W1(3)}

3. For Rank 5 and Rank 6:

C1={W1(0),W1(1),W1(2)}

4. For Rank 7:

C1={W1(0)}

5. For Rank 8:

C1={W1(0)}

Other Expressions
Detailed digits of the full first codebook C1 and the full second codebook C2 are expressed above using ans(;,;,n) for each of various ranks. The aforementioned expression scheme may be complex and thus, the full first codebook C1 and the full second codebook C2 are expressed below using a relatively simple expression scheme.
i1 may correspond to a first precoding matrix indicator and i2 may correspond to a second precoding matrix indicator. φn and νm may be expressed as follows:

φn=ejπn/2 

νm=[1ej2πn/32ej4πn/32ej6πn/32]T 

In this example, the first codebook C1 and the second codebook C2 for rank 1 may be simply expressed by the following tables. The following tables may represent the overall codebook C in which the first codebook C1 and the second codebook C2 are integrated.
First codebook C1 and second codebook C2 for rank 1:














i2















i1
0
1
2
3
4
5
6
7





0-15
W2i1,0(1)
W2i1,1(1)
W2i1,2(1)
W2i1,3(1)
W2i1+1,0(1)
W2i1+1,1(1)
W2i1+1,2(1)
W2i1+1,3(1)












i2















i1
8
9
10
11
12
13
14
15





0-14
W2i1+2,0(1)
W2i1+2,1(1)
W2i1+2,2(1)
W2i1+2,3(1)
W2i1+3,0(1)
W2i1+3,1(1)
W2i1+3,2(1)
W2i1+3,3(1)


15
W0,0(1)
W0,1(1)
W0,2(1)
W0,3(1)
W1,0(1)
W1,1(1)
W1,2(1)
W1,3(1)









  
    where
    ⁢
    
      
    
    ⁢
    
      W
      
        m
        ,
        n
      
      
        (
        1
        )
      
    
  
  =
  
    
      1
      
        8
      
    
    ⁡
    
      [
      
        
          
            
              v
              m
            
          
        
        
          
            
              
                φ
                n
              
              ⁢
              
                v
                m
              
            
          
        
      
      ]
    
  










First Codebook C1 and Second Codebook C2 for Rank 2:














i2











i1
0
1
2
3





0-14
W2i1,2i1,0(2)
W2i1,2i1,1(2)
W2i1+1,2i1+1,0(2)
W2i1+1,2i1+1,1(2)


15
W30,30,0(2)
W30,30,1(2)
W31,31,0(2)
W31,31,1(2)












i2











i1
4
5
6
7





0-14
W2i1+2,2i1+2,0(2)
W2i1+2,2i1+2,1(2)
W2i1+3,2i1+3,0(2)
W2i1+3,2i1+3,1(2)


15
W0,0,0(2)
W0,0,1(2)
W1,1,0(2)
W1,1,1(2)












i2











i1
8
9
10
11





0-14
W2i1,2i1+1,0(2)
W2i1,2i1+1,1(2)
W2i1+1,2i1+2,0(2)
W2i1+1,2i1+2,1(2)


15
W30,31,0(2)
W30,31,1(2)
W31,0,0(2)
W31,0,1(2)












i2











i1
12
13
14
15





0-14
W2i1,2i1+3,0(2)
W2i1,2i1+3,1(2)
W2i1+1,2i1+3,0(2)
W2i1+1,2i1+3,1(2)


15
W30,1,0(2)
W30,1,1(2)
W31,1,0(2)
W31,1,1(2)









  
    where
    ⁢
    
      
    
    ⁢
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        2
        )
      
    
  
  =
  
    
      1
      4
    
    ⁡
    
      [
      
        
          
            
              v
              m
            
          
          
            
              v
              
                m
                ′
              
            
          
        
        
          
            
              
                φ
                n
              
              ⁢
              
                v
                m
              
            
          
          
            
              
                -
                
                  φ
                  n
                
              
              ⁢
              
                v
                
                  m
                  ′
                
              
            
          
        
      
      ]
    
  










First Codebook C1 and Second Codebook C2 for Rank 3:














i2











i1
0
1
2
3





0-3
W4i1,4i1,4i1+4(3)
W4i1+4,4i1,4i1+4(3)
{tilde over (W)}4i1,4i1+4,4i1+4(3)
{tilde over (W)}4i1+4,4i1,4i1(3)












i2











i1
4
5
6
7





0-3
W4i1+1,4i1+1,4i1+5(3)
W4i1+5,4i1+1,4i1+5(3)
{tilde over (W)}4i1+1,4i1+5,4i1+5(3)
{tilde over (W)}4i1+5,4i1+1,4i1+1(3)












i2











i1
8
9
10
11





0-3
W4i1+2,4i1+2,4i1+6(3)
W4i1+6,4i1+2,4i1+6(3)
{tilde over (W)}4i1+2,4i1+6,4i1+6(3)
{tilde over (W)}4i1+6,4i1+2,4i1+2(3)












i2











i1
12
13
14
15





0-3
W4i1+3,4i1+3,4i1+7(3)
W4i1+7,4i1+3,4i1+7(3)
{tilde over (W)}4i1+3,4i1+7,4i1+7(3)
{tilde over (W)}4i1+7,4i1+3,4i1+3(3)









  
    
      where
      ⁢
      
        
      
      ⁢
      
        W
        
          m
          ,
          
            m
            ′
          
          ,
          
            m
            ′′
          
        
        
          (
          3
          )
        
      
    
    =
    
      
        1
        
          24
        
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
            
              
                v
                
                  m
                  ′′
                
              
            
          
          
            
              
                v
                m
              
            
            
              
                -
                
                  v
                  
                    m
                    ′
                  
                
              
            
            
              
                -
                
                  v
                  m
                
              
            
          
        
        ]
      
    
  
  ,






  
    
      W
      ~
    
    
      m
      ,
      
        m
        ′
      
      ,
      
        m
        ′′
      
    
    
      (
      3
      )
    
  
  =
  
    
      1
      
        24
      
    
    ⁡
    
      [
      
        
          
            
              v
              m
            
          
          
            
              v
              
                m
                ′
              
            
          
          
            
              v
              
                m
                ′′
              
            
          
        
        
          
            
              v
              m
            
          
          
            
              v
              
                m
                ′
              
            
          
          
            
              -
              
                v
                m
              
            
          
        
      
      ]
    
  










First Codebook C1 and Second Codebook C2 for Rank 4:














i2











i1
0
1
2
3





0-3
W4i1,4i1+4,0(4)
W4i1,4i1+4,1(4)
W4i1+1,4i1+5,0(4)
W4i1+1,4i1+5,1(4)












i2











i1
4
5
6
7





0-3
W4i1+2,4i1+6,0(4)
W4i1+2,4i1+6,1(4)
W4i1+3,4i1+7,0(4)
W4i1+3,4i1+7,1(4)









  
    where
    ⁢
    
      
    
    ⁢
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        4
        )
      
    
  
  =
  
    
      1
      
        32
      
    
    ⁡
    
      [
      
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ⁢
        
          
            
              
                v
                m
              
            
          
          
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  m
                
              
            
          
        
        ⁢
        
          
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
      
      ]
    
  










First Codebook C1 and Second Codebook C2 for Rank 5:














i1
i2










0



 



0-3




  
    W
    
      i
      1
    
    
      (
      5
      )
    
  
  =
  
    
      1
      
        40
      
    
    ⁡
    
      [
      
        
          
            
              v
              
                2
                ⁢
                
                  i
                  1
                
              
            
          
          
            
              v
              
                2
                ⁢
                
                  i
                  1
                
              
            
          
          
            
              v
              
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
                +
                8
              
            
          
          
            
              v
              
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
                +
                8
              
            
          
          
            
              v
              
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
                +
                16
              
            
          
        
        
          
            
              v
              
                2
                ⁢
                
                  i
                  1
                
              
            
          
          
            
              -
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
          
          
            
              v
              
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
                +
                8
              
            
          
          
            
              -
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
          
          
            
              v
              
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
                +
                16
              
            
          
        
      
      ]
    
  














First Codebook C1 and Second Codebook C2 for Rank 6:














i1
i2










0



 



0-3




  
    W
    
      i
      1
    
    
      (
      6
      )
    
  
  =
  
    
      1
      
        48
      
    
    ⁡
    
      [
      
        
          
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
          
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                -
                
                  v
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                -
                
                  v
                  
                    
                      2
                      ⁢
                      
                        i
                        1
                      
                    
                    +
                    8
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
        
        ⁢
        
          
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
          
            
              
                -
                
                  v
                  
                    
                      2
                      ⁢
                      
                        i
                        1
                      
                    
                    +
                    16
                  
                
              
            
          
        
      
      ]
    
  














First Codebook C1 and Second Codebook C2 for Rank 7:











i1
i2








0


 


0-3




  
    W
    
      i
      1
    
    
      (
      7
      )
    
  
  =
  
    
      1
      
        56
      
    
    ⁡
    
      [
      
        
          
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
          
            
              
                v
                
                  2
                  ⁢
                  
                    i
                    1
                  
                
              
            
            
              
                -
                
                  v
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  8
                
              
            
            
              
                -
                
                  v
                  
                    
                      2
                      ⁢
                      
                        i
                        1
                      
                    
                    +
                    8
                  
                
              
            
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
        
        ⁢
        
          
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  16
                
              
            
          
          
            
              
                -
                
                  v
                  
                    
                      2
                      ⁢
                      
                        i
                        1
                      
                    
                    +
                    16
                  
                
              
            
          
        
        ⁢
        
          
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  24
                
              
            
          
          
            
              
                v
                
                  
                    2
                    ⁢
                    
                      i
                      1
                    
                  
                  +
                  24
                
              
            
          
        
      
      ]
    
  













First Codebook C1 and Second Codebook C2 for Rank 8:











i1
i2








0


 


0




  
    
      
        
          
            W
            
              i
              1
            
            
              (
              8
              )
            
          
          =
        
      
    
    
      
        
          
            
              1
              8
            
            ⁡
            
              [
              
                
                  
                    
                      
                        v
                        
                          2
                          ⁢
                          
                            i
                            1
                          
                        
                      
                    
                    
                      
                        v
                        
                          2
                          ⁢
                          
                            i
                            1
                          
                        
                      
                    
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          8
                        
                      
                    
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          8
                        
                      
                    
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          16
                        
                      
                    
                  
                  
                    
                      
                        v
                        
                          2
                          ⁢
                          
                            i
                            1
                          
                        
                      
                    
                    
                      
                        -
                        
                          v
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                        
                      
                    
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          8
                        
                      
                    
                    
                      
                        -
                        
                          v
                          
                            
                              2
                              ⁢
                              
                                i
                                1
                              
                            
                            +
                            8
                          
                        
                      
                    
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          16
                        
                      
                    
                  
                
                ⁢
                
                  
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          16
                        
                      
                    
                  
                  
                    
                      
                        -
                        
                          v
                          
                            
                              2
                              ⁢
                              
                                i
                                1
                              
                            
                            +
                            16
                          
                        
                      
                    
                  
                
                ⁢
                
                  
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          24
                        
                      
                    
                  
                  
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          24
                        
                      
                    
                  
                
                ⁢
                
                  
                    
                      
                        v
                        
                          
                            2
                            ⁢
                            
                              i
                              1
                            
                          
                          +
                          24
                        
                      
                    
                  
                  
                    
                      
                        -
                        
                          v
                          
                            
                              2
                              ⁢
                              
                                i
                                1
                              
                            
                            +
                            24
                          
                        
                      
                    
                  
                
              
              ]
            
          
           
        
      
    
  
   













The aforementioned simple expression of the full first codebook C1 and the full second codebook C2 may also be applicable to the subset of the first codebook C1 and the subset of the second codebook C2.
A. Subset of First Codebook and Subset of Second Codebook for PUCCH 2-1 Sub-Mode 1:
i. For ranks 2, 3, and 4, when the subset of the first codebook includes four bits and the subset of the second codebook includes two bits:
The subset of the first codebook and the subset of the second codebook for rank r may be defined by selecting subsequent i1 and/or i2 from the full first codebook C1 and the full second codebook C2 for rank r that are described above.
For example, the following subset of the first codebook and the subset of the second codebook for rank 2 may be defined by selecting i2={0,1,4,5} or {0,2,4,6} from the full first codebook C1 and the full second codebook C2 for rank 2.
1. For Rank 2:

i2={0,1,4,5} or {0,2,4,6}

2. For Rank 3:

i2={0,4,8,12} or {1,5,9,13} or {2,6,10,14} or {3,7,11,15}

3. For Rank 4:

i2={0,2,4,6} or {0,1,4,5} or {2,3,6,7}

B. Subset of First Codebook and Subset of Second Codebook for PUCCH 1-1 Sub-Mode 2:
i. For Ranks 3 and 4, when the Subset of the First Codebook Includes a Single Bit and the Subset of the Second Codebook Includes Three Bits:
1. For Rank 3:

i1={0,2} or {1,3}

i2={0,1,2,3,8,9,10,11}

2. For Rank 4:

i1={0,2} or {1,3}

i2={0,1,2,3,4,5,6,7}

ii. When the Subset of the First Codebook Includes Two Bits and the Subset of the Second Codebook Includes Two Bits:
1. For Rank 1:

i1={0,4,8,12} or {2,6,10,14}

i2={0,1,8,9} or {4,5,12,13} or {0,4,8,12}

2. For Rank 2:

i1={0,4,8,12} or {2,6,10,14}

i2={0,1,4,5} or {2,3,6,7} or {0,2,4,6}

3. For Rank 3:

i1={0,1,2,3}

i2={0,4,8,12} or {1,5,9,13} or {2,6,10,14} or {3,7,11,15}

4. For Rank 4:

i1={0,1,2,3}

i2={0,2,4,6} or {0,1,4,5} or {2,3,6,7}

iii. When the Subset of the First Codebook Includes Three Bits and the Subset of the Second Codebook Includes a Single Bit:
1. For Rank 1:

i1={0,2,4,6,8,10,12,14}

i2={0,8} or {0,1} or {4,5} or {8,9} or {12,13} or {0,2} or {4,6} or {8,10} or {12,14}

2. For Rank 2:

i1={0,2,4,6,8,10,12,14}

i2={0,1} or {2,3} or {4,5} or {6,7} or {0,4} or {2,6}

3. For Rank 3 and Rank 4:
The subset C1 of the first codebook and the subset C2 of the second codebook for rank 3 and rank 4 may be the same as the subset C1 of the two-bit first codebook and the subset C2 of the two-bit second codebook that are described above.
iv. When the Subset of the First Codebook Includes Four Bits and the Subset of the Second Codebook Includes Zero Bit:
1. For Rank 1:

i1={0,1,2, . . . ,16}

i2={0} or {4} or {8} or {12}

or i1={0,2,4, . . . ,14} with i2={0} and i1={1,3,5, . . . ,15} with i2={2}

2. For Rank 2:

i1={0,1,2, . . . ,16}

i2={0} or {2} or {4} or {6}

3. For Rank 3 and Rank 4:
The subset C1 of the first codebook and the subset C2 of the second codebook for rank 3 and rank 4 may be the same as the subset C1 of the two-bit first codebook and the subset C2 of the two-bit second codebook that are described above.
C. Subset of First Codebook for PUCCH 1-1 Sub-Mode 1 when a Rank Indicator and a First Precoding Matrix Indicator are Commonly Encoded:
i. Five Bits of Common Encoding of Rank Indicator and First Precoding Matrix Indicator—Example 1:
1. For Rank 1 and Rank 2:

i1={0,2,4, . . . ,14} or i1={1,3,5, . . . ,15}

2. For Rank 3 and Rank 4:

i1={0,2} or i1={1,3}

3. For Rank 5 and Rank 6:

i1={0,1,2,3}

4. For Rank 7:

i1={0,12}

5. For Rank 8:

i1={0}

ii. Five Bits of Common Encoding of Rank Indicator and First Precoding Matrix Indicator—Example 2:
1. For Rank 1 and Rank 2:

i1={0,2,4, . . . ,14} or i1={1,3,5, . . . ,15}

2. For Rank 3 and Rank 4:

i1={0,1,2,3}

3. For Rank 5 and Rank 5:

i1={0,1,2}

4. For Rank 7:

i1={0}

5. For Rank 8:

i1={0}

Description related to the subset of the first codebook and the subset of the second codebook varying based on a reporting mode is described above.
Detailed digits of the subset of the first codebook and the subset of the second codebook with respect to some reporting modes may follow as:
1. Subset of First Codebook and Subset of Second Codebook in PUCCH 1-1 Sub-Mode 2:
(1) For Rank 1:
For example, when the subset of the first codebook includes three bits and the subset of the second codebook includes a single bit, the subset of the first codebook may include ans(;,;,n=1), ans(;,;,n=3), ans(;,;,n=5), ans(;,;,n=7), ans(;,;,n=9), ans(;,;,n=11), ans(;,;,n=13), and ans(;,;,n=15) that are described above.
That is, codewords included in the subset of the first codebook may be expressed as follows:












ans(:, :, 1) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i


   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i


   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


   0.5000
  0.4904 + 0.0975i
  0.4619 + 0.1913i
  0.4157 + 0.2778i


   0.5000
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i


   0.5000
  0.4157 + 0.2778i
  0.1913 + 0.4619i
−0.0975 + 0.4904i







ans(:, :, 3) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i


  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i


−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


  0.3536 + 0.3536i
  0.2778 + 0.4157i
  0.1913 + 0.4619i
  0.0975 + 0.4904i


  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i


−0.3536 + 0.3536i
−0.4904 + 0.0975i
−0.4619 − 0.1913i
−0.2778 − 0.4157i







ans(:, :, 5) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i


−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i


−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


  0.0000 + 0.5000i
−0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.2778 + 0.4157i


−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i


−0.0000 − 0.5000i
  0.2778 − 0.4157i
  0.4619 − 0.1913i
  0.4904 + 0.0975i







ans(:, :, 7) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i


−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i


  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


−0.3536 + 0.3536i
−0.4157 + 0.2778i
−0.4619 + 0.1913i
−0.4904 + 0.0975i


−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i


  0.3536 + 0.3536i
  0.0975 + 0.4904i
−0.1913 + 0.4619i
−0.4157 + 0.2778i







ans(:, :, 9) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i


  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i


−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


−0.5000 + 0.0000i
−0.4904 − 0.0975i
−0.4619 − 0.1913i
−0.4157 − 0.2778i


  0.5000 − 0.0000i
  0.4619 + 0.1913i
  0.3536 + 0.3536i
  0.1913 + 0.4619i


−0.5000 + 0.0000i
−0.4157 − 0.2778i
−0.1913 − 0.4619i
  0.0975 − 0.4904i







ans(:, :, 11) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i


  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i


  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


−0.3536 − 0.3536i
−0.2778 − 0.4157i
−0.1913 − 0.4619i
−0.0975 − 0.4904i


  0.0000 + 0.5000i
−0.1913 + 0.4619i
−0.3536 + 0.3536i
−0.4619 + 0.1913i


  0.3536 − 0.3536i
  0.4904 − 0.0975i
  0.4619 + 0.1913i
  0.2778 + 0.4157i







ans(:, :, 13) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i


−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i


  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


−0.0000 − 0.5000i
  0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.2778 − 0.4157i


−0.5000 + 0.0000i
−0.4619 − 0.1913i
−0.3536 − 0.3536i
−0.1913 − 0.4619i


  0.0000 + 0.5000i
−0.2778 + 0.4157i
−0.4619 + 0.1913i
−0.4904 − 0.0975i







ans(:, :, 15) =


columns 1-4










   0.5000
   0.5000
   0.5000
   0.5000


  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i


−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i


−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i


0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0







columns 5-8










0
0
0
0


0
0
0
0


0
0
0
0


0
0
0
0


   0.5000
   0.5000
   0.5000
   0.5000


  0.3536 − 0.3536i
  0.4157 − 0.2778i
  0.4619 − 0.1913i
  0.4904 − 0.0975i


−0.0000 − 0.5000i
  0.1913 − 0.4619i
  0.3536 − 0.3536i
  0.4619 − 0.1913i


−0.3536 − 0.3536i
−0.0975 − 0.4904i
  0.1913 − 0.4619i
  0.4157 − 0.2778i









The subset of the second codebook may include (;,;,n=1) and (;,;,n=3) for rank 1 that are described above.
That is, codewords included in the subset of the second codebook may be expressed as follows:












(:, :, 1) =


0.7071


0


0


0


0.7071


0


0


0


(:, :, 3) =


0.7071


0


0


0


−0.7071


0


0


0









A combination of a first precoding matrix indicator selected from the subset of the first codebook and a second precoding matrix indicator selected from the subset of the second codebook may indicate one of precoding matrix candidates disclosed in the following overall codebook.












ans(:, :, 1, 1) =


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


  0.3536


ans(:, :, 3, 1) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


ans(:, :, 5, 1) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


ans(:, :, 7, 1) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


ans(:, :, 9, 1) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


ans(:, :, 11, 1) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


ans(:, :, 13, 1) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


ans(:, :, 15, 1) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


ans(:, :, 1, 3) =


  0.3536


  0.3536


  0.3536


  0.3536


−0.3536


−0.3536


−0.3536


−0.3536


ans(:, :, 3, 3) =


  0.3536


  0.2500 + 0.2500i


  0.0000 + 0.3536i


−0.2500 + 0.2500i


−0.3536


−0.2500 − 0.2500i


−0.0000 − 0.3536i


  0.2500 − 0.2500i


ans(:, :, 5, 3) =


  0.3536


  0.0000 + 0.3536i


−0.3536 + 0.0000i


−0.0000 − 0.3536i


−0.3536


−0.0000 − 0.3536i


  0.3536 − 0.0000i


  0.0000 + 0.3536i


ans(:, :, 7, 3) =


  0.3536


−0.2500 + 0.2500i


−0.0000 − 0.3536i


  0.2500 + 0.2500i


−0.3536


  0.2500 − 0.2500i


  0.0000 + 0.3536i


−0.2500 − 0.2500i


ans(:, :, 9, 3) =


  0.3536


−0.3536 + 0.0000i


  0.3536 − 0.0000i


−0.3536 + 0.0000i


−0.3536


  0.3536 − 0.0000i


−0.3536 + 0.0000i


  0.3536 − 0.0000i


ans(:, :, 11, 3) =


  0.3536


−0.2500 − 0.2500i


  0.0000 + 0.3536i


  0.2500 − 0.2500i


−0.3536


  0.2500 + 0.2500i


−0.0000 − 0.3536i


−0.2500 + 0.2500i


ans(:, :, 13, 3) =


  0.3536


−0.0000 − 0.3536i


−0.3536 + 0.0000i


  0.0000 + 0.3536i


−0.3536


  0.0000 + 0.3536i


  0.3536 − 0.0000i


−0.0000 − 0.3536i


ans(:, :, 15, 3) =


  0.3536


  0.2500 − 0.2500i


−0.0000 − 0.3536i


−0.2500 − 0.2500i


−0.3536


−0.2500 + 0.2500i


  0.0000 + 0.3536i


  0.2500 + 0.2500i









As described above, in PUCCH 1-1 sub-mode 2, the subset of the first codebook and the subset of the second codebook for rank 1 may be variuosly determined and thus, the overall codebook may also be determined to be different from Table 1.
(2) For Rank 2:
For example, when the subset of the first codebook includes three bits and the subset of the second codebook includes a single bit, the subset of the first codebook may include ans(;,;,n=1), ans(;,;,n=3), ans(;,;,n=5), ans(;,;,n=7), ans(;,;,n=9), ans(;,;,n=11), ans(;,;,n=13), and ans(;,;,n=15) that are described above. Detailed digits of codewords included in the subset of the first codebook are described above. The subset of the second codebook may include (;,;,n=1) and (;,;,n=2) for rank 2 that are described above.
That is, the codewords included in the subset of the second codebook may be expressed as follows:












(:, :, 1) =










   0.5000
0.5000



0
0



0
0



0
0



   0.5000
−0.5000



0
0



0
0



0
0







(:, :, 2) =










   0.5000
0.5000



0
0



0
0



0
0



0 + 0.5000i
0 − 0.5000i



0
0



0
0



0
0










The combination of the first precoding matrix indicator selected from the subset of the first codebook and the second precoding matrix indicator selected from the subset of the second codebook may indicate one of precoding matrix candidates disclosed in the following overall codebook.












ans(:, :, 1, 1) =










0.2500
  0.2500



0.2500
  0.2500



0.2500
  0.2500



0.2500
  0.2500



0.2500
−0.2500



0.2500
−0.2500



0.2500
−0.2500



0.2500
−0.2500







ans(:, :, 3, 1) =










0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



0.2500
−0.2500



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 5, 1) =










0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



0.2500
−0.2500



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 7, 1) =










0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



0.2500
−0.2500



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 9, 1) =










0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



0.2500
−0.2500



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 11, 1) =










0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



0.2500
−0.2500



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 13, 1) =










0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



0.2500
−0.2500



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.0000 + 0.2500i
−0.0000 − 0.2500i







ans(:, :, 15, 1) =










0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



0.2500
−0.2500



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 1, 2) =










0.2500
  0.2500



0.2500
  0.2500



0.2500
  0.2500



0.2500
  0.2500



    0 + 0.2500i
    0 − 0.2500i



    0 + 0.2500i
    0 − 0.2500i



    0 + 0.2500i
    0 − 0.2500i



    0 + 0.2500i
    0 − 0.2500i







ans(:, :, 3, 2) =










0.2500
  0.2500



  0.1768 + 0.1768i
  0.1768 + 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i
−0.1768 + 0.1768i



    0 + 0.2500i
    0 − 0.2500i



−0.1768 + 0.1768i
  0.1768 − 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.1768 − 0.1768i
  0.1768 + 0.1768i







ans(:, :, 5, 2) =










0.2500
  0.2500



  0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



    0 + 0.2500i
    0 − 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i







ans(:, :, 7, 2) =










0.2500
  0.2500



−0.1768 + 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



  0.1768 + 0.1768i
  0.1768 + 0.1768i



    0 + 0.2500i
    0 − 0.2500i



−0.1768 − 0.1768i
  0.1768 + 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.1768 + 0.1768i
  0.1768 − 0.1768i







ans(:, :, 9, 2) =










0.2500
  0.2500



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



    0 + 0.2500i
    0 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



  0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.0000 − 0.2500i
  0.0000 + 0.2500i







ans(:, :, 11, 2) =










0.2500
  0.2500



−0.1768 − 0.1768i
−0.1768 − 0.1768i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



  0.1768 − 0.1768i
  0.1768 − 0.1768i



    0 + 0.2500i
    0 − 0.2500i



  0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.2500 + 0.0000i
  0.2500 − 0.0000i



  0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 13, 2) =










0.2500
  0.2500



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i
−0.2500 + 0.0000i



  0.0000 + 0.2500i
  0.0000 + 0.2500i



    0 + 0.2500i
    0 − 0.2500i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.0000 − 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i
  0.2500 − 0.0000i







ans(:, :, 15, 2) =










0.2500
  0.2500



  0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i
−0.0000 − 0.2500i



−0.1768 − 0.1768i
−0.1768 − 0.1768i



    0 + 0.2500i
    0 − 0.2500i



  0.1768 + 0.1768i
−0.1768 − 0.1768i



  0.2500 − 0.0000i
−0.2500 + 0.0000i



  0.1768 − 0.1768i
−0.1768 + 0.1768i










FIG. 5 illustrates an example of a communication method of a transmitter and a receiver that operate in PUCCH 1-1 sub-mode 2.
At 510, the transmitter and the receiver may determine a subset of a first codebook and a subset of a second codebook that are described above. The subset of the first codebook and the subset of the second codebook may be individually stored in the transmitter and the receiver. The overall codebook in which the subset of the first codebook and the subset of the second codebook are integrated may be stored in the transmitter and the receiver.
At 520, the receiver may select a single codeword from the subset of the first codebook or the overall codebook and extract the selected codeword as a first precoding matrix indicator, and may select a single codeword from the subset of the second codebook or the overall codebook and extract the selected codeword as the second precoding matrix indicator.
At 530, the receiver may feed back the first precoding matrix indicator and the second precoding matrix indicator to the transmitter. The receiver may further feed back a rank indicator and CQI_s.
At 540, the transmitter may calculate W by performing inner product between W1 and W2. W1 may be present in the subset of the first codebook and be indicated by the first precoding matrix indicator, and W2 may be present in the subset of the second codebook and be indicated by the second precoding matrix indicator.
At 550, the transmitter may precode a data stream based on the precoding matrix W. At 560, the transmitter may transmit data.
2. Subset of First Codebook and Subset of Second Codebook in PUCCH 2-1 Sub-Mode 1, 2:
(1) For Rank 2:
For example, the subset of the first codebook may include ans(;,;,n=1), ans(;,;,n=2), ans(;,;,n=3), . . . , ans(;,;,n=16) for rank 2 that are described above.
The subset of the second codebook may include (;,;, n=1), (;,;, n=3), (;,;, n=5), and (;,;, n=7) for rank 2 that are described above. That is, detailed codewords of the subset of the second codebook may be expressed as follows:












(:, :, 1) =










0.5000
0.5000



0
0



0
0



0
0



0.5000
−0.5000



0
0



0
0



0
0







(:, :, 3) =










0
0



0.5000
0.5000



0
0



0
0



0
0



0.5000
−0.5000



0
0



0
0







(:, :, 5) =










0
0



0
0



0.5000
0.5000



0
0



0
0



0
0



0.5000
−0.5000



0
0







(:, :, 7) =










0
0



0
0



0
0



0.5000
0.5000



0
0



0
0



0
0



0.5000
−0.5000










The combination of the first precoding matrix indicator selected from the subset of the first codebook and the second precoding matrix indicator selected from the subset of the second codebook may indicate one of precoding matrix candidates disclosed in the following overall codebook.












ans(:, :, 1, 1) =










0.2500
0.2500



0.2500
0.2500



0.2500
0.2500



0.2500
0.2500



0.2500
−0.2500  



0.2500
−0.2500  



0.2500
−0.2500  



0.2500
−0.2500  







ans(:, :, 2, 1) =










0.2500
0.2500



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.0957 + 0.2310i
  0.0957 + 0.2310i



0.2500
−0.2500  



0.2310 + 0.0957i
−0.2310 − 0.0957i



0.1768 + 0.1768i
−0.1768 − 0.1768i



0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 3, 1) =










0.2500
0.2500



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



0.2500
−0.2500  



0.1768 + 0.1768i
−0.1768 − 0.1768i



0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i







ans(:, :, 4, 1) =










0.2500
0.2500



0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.2500
−0.2500  



0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i







ans(:, :, 5, 1) =










0.2500
0.2500



0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



−0.0000 − 0.2500i  
− 0.0000 − 0.2500i



0.2500
−0.2500  



0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i







ans(:, :, 6, 1) =










0.2500
0.2500



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.2500
−0.2500  



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 7, 1) =










0.2500
0.2500



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.2500
−0.2500  



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 8, 1) =










0.2500
0.2500



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



0.2500
−0.2500  



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i







ans(:, :, 9, 1) =










0.2500
0.2500



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.2500
−0.2500  



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i







ans(:, :, 10, 1) =










0.2500
0.2500



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



0.2500
−0.2500  



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i







ans(:, :, 11, 1) =










0.2500
0.2500



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.0000 + 0.2500i
  0.0000 + 0.2500i



0.1768 − 0.1768i
  0.1768 − 0.1768i



0.2500
−0.2500  



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



0.0000 + 0.2500i
−0.0000 − 0.2500i



0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 12, 1) =










0.2500
0.2500



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.2500
−0.2500  



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 13, 1) =










0.2500
0.2500



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.0000 + 0.2500i
  0.0000 + 0.2500i



0.2500
−0.2500  



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



0.0000 + 0.2500i
−0.0000 − 0.2500i







ans(:, :, 14, 1) =










0.2500
0.2500



0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.2500
−0.2500  



0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i







ans(:, :, 15, 1) =










0.2500
0.2500



0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.2500
−0.2500  



0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i







ans(:, :, 16, 1) =










0.2500
0.2500



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.1768 − 0.1768i
  0.1768 − 0.1768i



0.0957 − 0.2310i
  0.0957 − 0.2310i



0.2500
−0.2500  



0.2310 − 0.0957i
−0.2310 + 0.0957i



0.1768 − 0.1768i
−0.1768 + 0.1768i



0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 1, 3) =










0.2500
0.2500



0.2452 + 0.0488i
  0.2452 + 0.0488i



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.2079 + 0.1389i
  0.2079 + 0.1389i



0.2500
−0.2500  



0.2452 + 0.0488i
−0.2452 − 0.0488i



0.2310 + 0.0957i
−0.2310 − 0.0957i



0.2079 + 0.1389i
−0.2079 − 0.1389i







ans(:, :, 2, 3) =










0.2500
0.2500



0.2079 + 0.1389i
  0.2079 + 0.1389i



0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i  
−0.0488 + 0.2452i



0.2500
−0.2500  



0.2079 + 0.1389i
−0.2079 − 0.1389i



0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.0488 + 0.2452i  
  0.0488 − 0.2452i







ans(:, :, 3, 3) =










0.2500
0.2500



0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



−0.2452 + 0.0488i  
−0.2452 + 0.0488i



0.2500
−0.2500  



0.1389 + 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



−0.2452 + 0.0488i  
  0.2452 − 0.0488i







ans(:, :, 4, 3) =










0.2500
0.2500



0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



−0.1389 − 0.2079i  
−0.1389 − 0.2079i



0.2500
−0.2500  



0.0488 + 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



−0.1389 − 0.2079i  
  0.1389 + 0.2079i







ans(:, :, 5, 3) =










0.2500
0.2500



−0.0488 + 0.2452i  
−0.0488 + 0.2452i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.1389 − 0.2079i
  0.1389 − 0.2079i



0.2500
−0.2500  



−0.0488 + 0.2452i  
  0.0488 − 0.2452i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 6, 3) =










0.2500
0.2500



−0.1389 + 0.2079i  
−0.1389 + 0.2079i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



0.2452 + 0.0488i
  0.2452 + 0.0488i



0.2500
−0.2500  



−0.1389 + 0.2079i  
  0.1389 − 0.2079i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 7, 3) =










0.2500
0.2500



−0.2079 + 0.1389i  
−0.2079 + 0.1389i



0.0957 − 0.2310i
  0.0957 − 0.2310i



0.0488 + 0.2452i
  0.0488 + 0.2452i



0.2500
−0.2500  



−0.2079 + 0.1389i  
  0.2079 − 0.1389i



0.0957 − 0.2310i
−0.0957 + 0.2310i



0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 8, 3) =










0.2500
0.2500



−0.2452 + 0.0488i  
−0.2452 + 0.0488i



0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i  
−0.2079 + 0.1389i



0.2500
−0.2500  



−0.2452 + 0.0488i  
  0.2452 − 0.0488i



0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.2079 + 0.1389i  
  0.2079 − 0.1389i







ans(:, :, 9, 3) =










0.2500
0.2500



−0.2452 − 0.0488i  
−0.2452 − 0.0488i



0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i  
−0.2079 − 0.1389i



0.2500
−0.2500  



−0.2452 − 0.0488i  
  0.2452 + 0.0488i



0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2079 − 0.1389i  
  0.2079 + 0.1389i







ans(:, :, 10, 3) =










0.2500
0.2500



−0.2079 − 0.1389i  
−0.2079 − 0.1389i



0.0957 + 0.2310i
  0.0957 + 0.2310i



0.0488 − 0.2452i
  0.0488 − 0.2452i



0.2500
−0.2500  



−0.2079 − 0.1389i  
  0.2079 + 0.1389i



0.0957 + 0.2310i
−0.0957 − 0.2310i



0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 11, 3) =










0.2500
0.2500



−0.1389 − 0.2079i  
−0.1389 − 0.2079i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



0.2452 − 0.0488i
  0.2452 − 0.0488i



0.2500
−0.2500  



−0.1389 − 0.2079i  
  0.1389 + 0.2079i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 12, 3) =










0.2500
0.2500



−0.0488 − 0.2452i  
−0.0488 − 0.2452i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.1389 + 0.2079i
  0.1389 + 0.2079i



0.2500
−0.2500  



−0.0488 −0.2452i  
  0.0488 + 0.2452i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 13, 3) =










0.2500
0.2500



0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



−0.1389 + 0.2079i  
−0.1389 + 0.2079i



0.2500
−0.2500  



0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



−0.1389 + 0.2079i  
  0.1389 − 0.2079i







ans(:, :, 14, 3) =










0.2500
0.2500



0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



−0.2452 − 0.0488i  
−0.2452 − 0.0488i



0.2500
−0.2500  



0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



−0.2452 − 0.0488i  
  0.2452 + 0.0488i







ans(:, :, 15, 3) =










0.2500
0.2500



0.2079 − 0.1389i
  0.2079 − 0.1389i



0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i  
−0.0488 − 0.2452i



0.2500
−0.2500  



0.2079 − 0.1389i
−0.2079 + 0.1389i



0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.0488 − 0.2452i  
  0.0488 + 0.2452i







ans(:, :, 16, 3) =










0.2500
0.2500



0.2452 − 0.0488i
  0.2452 − 0.0488i



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.2079 − 0.1389i
  0.2079 − 0.1389i



0.2500
−0.2500  



0.2452 − 0.0488i
−0.2452 + 0.0488i



0.2310 − 0.0957i
−0.2310 + 0.0957i



0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 1, 5) =










0.2500
0.2500



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.0957 + 0.2310i
  0.0957 + 0.2310i



0.2500
−0.2500  



0.2310 + 0.0957i
−0.2310 − 0.0957i



0.1768 + 0.1768i
−0.1768 − 0.1768i



0.0957 + 0.2310i
−0.0957 − 0.2310i







ans(:, :, 2, 5) =










0.2500
0.2500



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



0.2500
−0.2500  



0.1768 + 0.1768i
−0.1768 − 0.1768i



0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i







ans(:, :, 3, 5) =










0.2500
0.2500



0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.2500
−0.2500  



0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i







ans(:, :, 4, 5) =










0.2500
0.2500



0.0000 + 0.2500i
  0.0000 + 0.2500i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



0.2500
−0.2500  



0.0000 + 0.2500i
−0.0000 − 0.2500i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i







ans(:, :, 5, 5) =










0.2500
0.2500



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.2500
−0.2500  



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



0.2310 − 0.0957i
−0.2310 + 0.0957i







ans(:, :, 6, 5) =










0.2500
0.2500



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



0.1768 + 0.1768i
  0.1768 + 0.1768i



0.2500
−0.2500  



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



0.1768 + 0.1768i
−0.1768 − 0.1768i







ans(:, :, 7, 5) =










0.2500
0.2500



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



0.2500
−0.2500  



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i







ans(:, :, 8, 5) =










0.2500
0.2500



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.2500 − 0.0000i
  0.2500 − 0.0000i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.2500
−0.2500  



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



0.2500 − 0.0000i
−0.2500 + 0.0000i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i







ans(:, :, 9, 5) =










0.2500
0.2500



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.1768 + 0.1768i
  0.1768 + 0.1768i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



0.2500
−0.2500  



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



0.1768 + 0.1768i
−0.1768 − 0.1768i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i







ans(:, :, 10, 5) =










0.2500
0.2500



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.0000 + 0.2500i
  0.0000 + 0.2500i



0.1768 − 0.1768i
  0.1768 − 0.1768i



0.2500
−0.2500  



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



0.0000 + 0.2500i
−0.0000 − 0.2500i



0.1768 − 0.1768i
−0.1768 + 0.1768i







ans(:, :, 11, 5) =










0.2500
0.2500



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



−0.1768 + 0.1768i  
−0.1768 + 0.1768i



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.2500
−0.2500  



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



−0.1768 + 0.1768i  
  0.1768 − 0.1768i



0.2310 + 0.0957i
−0.2310 − 0.0957i







ans(:, :, 12, 5) =










0.2500
0.2500



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



−0.2500 + 0.0000i  
−0.2500 + 0.0000i



0.0000 + 0.2500i  
  0.0000 + 0.2500i



0.2500
−0.2500  



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



−0.2500 + 0.0000i  
  0.2500 − 0.0000i



0.0000 + 0.2500i
−0.0000 − 0.2500i







ans(:, :, 13, 5) =










0.2500
0.2500



0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.2500
−0.2500  



0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i







ans(:, :, 14, 5) =










0.2500
0.2500



0.1768 − 0.1768i
  0.1768 − 0.1768i



−0.0000 − 0.2500i  
−0.0000 − 0.2500i



−0.1768 − 0.1768i  
−0.1768 − 0.1768i



0.2500
−0.2500  



0.1768 − 0.1768i
−0.1768 + 0.1768i



−0.0000 − 0.2500i  
  0.0000 + 0.2500i



−0.1768 − 0.1768i  
  0.1768 + 0.1768i







ans(:, :, 15, 5) =










0.2500
0.2500



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.1768 − 0.1768i
  0.1768 − 0.1768i



0.0957 − 0.2310i
  0.0957 − 0.2310i



0.2500
−0.2500  



0.2310 − 0.0957i
−0.2310 + 0.0957i



0.1768 − 0.1768i
−0.1768 + 0.1768i



0.0957 − 0.2310i
−0.0957 + 0.2310i







ans(:, :, 16, 5) =










0.2500
0.2500



0.2500
0.2500



0.2500
0.2500



0.2500
0.2500



0.2500
−0.2500  



0.2500
−0.2500  



0.2500
−0.2500  



0.2500
−0.2500  







ans(:, :, 1, 7) =










0.2500
0.2500



0.2079 + 0.1389i
  0.2079 + 0.1389i



0.0957 + 0.2310i
  0.0957 + 0.2310i



−0.0488 + 0.2452i  
−0.0488 + 0.2452i



0.2500
−0.2500  



0.2079 + 0.1389i
−0.2079 − 0.1389i



0.0957 + 0.2310i
−0.0957 − 0.2310i



−0.0488 + 0.2452i  
  0.0488 − 0.2452i







ans(:, :, 2, 7) =










0.2500
0.2500



0.1389 + 0.2079i
  0.1389 + 0.2079i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



−0.2452 + 0.0488i  
−0.2452 + 0.0488i



0.2500
−0.2500  



0.1389 + 0.2079i
−0.1389 − 0.2079i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



−0.2452 + 0.0488i  
  0.2452 − 0.0488i







ans(:, :, 3, 7) =










0.2500
0.2500



0.0488 + 0.2452i
  0.0488 + 0.2452i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



−0.1389 − 0.2079i  
−0.1389 − 0.2079i



0.2500
−0.2500  



0.0488 + 0.2452i
−0.0488 − 0.2452i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



−0.1389 − 0.2079i  
  0.1389 + 0.2079i







ans(:, :, 4, 7) =










0.2500
0.2500



−0.0488 + 0.2452i  
−0.0488 + 0.2452i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



0.1389 − 0.2079i
  0.1389 − 0.2079i



0.2500
−0.2500  



−0.0488 + 0.2452i  
  0.0488 − 0.2452i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



0.1389 − 0.2079i
−0.1389 + 0.2079i







ans(:, :, 5, 7) =










0.2500
0.2500



−0.1389 + 0.2079i  
−0.1389 + 0.2079i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



0.2452 + 0.0488i
  0.2452 + 0.0488i



0.2500
−0.2500  



−0.1389 + 0.2079i  
  0.1389 − 0.2079i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



0.2452 + 0.0488i
−0.2452 − 0.0488i







ans(:, :, 6, 7) =










0.2500
0.2500



−0.2079 + 0.1389i  
−0.2079 + 0.1389i



0.0957 − 0.2310i
  0.0957 − 0.2310i



0.0488 + 0.2452i
  0.0488 + 0.2452i



0.2500
−0.2500  



−0.2079 + 0.1389i  
  0.2079 − 0.1389i



0.0957 − 0.2310i
−0.0957 + 0.2310i



0.0488 + 0.2452i
−0.0488 − 0.2452i







ans(:, :, 7, 7) =










0.2500
0.2500



−0.2452 + 0.0488i  
−0.2452 + 0.0488i



0.2310 − 0.0957i
  0.2310 − 0.0957i



−0.2079 + 0.1389i  
−0.2079 + 0.1389i



0.2500
−0.2500  



−0.2452 + 0.0488i  
  0.2452 − 0.0488i



0.2310 − 0.0957i
−0.2310 + 0.0957i



−0.2079 + 0.1389i  
  0.2079 − 0.1389i







ans(:, :, 8, 7) =










0.2500
0.2500



−0.2452 − 0.0488i  
−0.2452 − 0.0488i



0.2310 + 0.0957i
  0.2310 + 0.0957i



−0.2079 − 0.1389i  
−0.2079 − 0.1389i



0.2500
−0.2500  



−0.2452 − 0.0488i  
  0.2452 + 0.0488i



0.2310 + 0.0957i
−0.2310 − 0.0957i



−0.2079 − 0.1389i  
  0.2079 + 0.1389i







ans(:, :, 9, 7) =










0.2500
0.2500



−0.2079 − 0.1389i  
−0.2079 − 0.1389i



0.0957 + 0.2310i
  0.0957 + 0.2310i



0.0488 − 0.2452i
  0.0488 − 0.2452i



0.2500
−0.2500  



−0.2079 − 0.1389i  
  0.2079 + 0.1389i



0.0957 + 0.2310i
−0.0957 − 0.2310i



0.0488 − 0.2452i
−0.0488 + 0.2452i







ans(:, :, 10, 7) =










0.2500
0.2500



−0.1389 − 0.2079i  
−0.1389 − 0.2079i



−0.0957 + 0.2310i  
−0.0957 + 0.2310i



0.2452 − 0.0488i
  0.2452 − 0.0488i



0.2500
−0.2500  



−0.1389 − 0.2079i  
  0.1389 + 0.2079i



−0.0957 + 0.2310i  
  0.0957 − 0.2310i



0.2452 − 0.0488i
−0.2452 + 0.0488i







ans(:, :, 11, 7) =










0.2500
0.2500



−0.0488 − 0.2452i  
−0.0488 − 0.2452i



−0.2310 + 0.0957i  
−0.2310 + 0.0957i



0.1389 + 0.2079i
  0.1389 + 0.2079i



0.2500
−0.2500  



−0.0488 − 0.2452i  
  0.0488 + 0.2452i



−0.2310 + 0.0957i  
  0.2310 − 0.0957i



0.1389 + 0.2079i
−0.1389 − 0.2079i







ans(:, :, 12, 7) =










0.2500
0.2500



0.0488 − 0.2452i
  0.0488 − 0.2452i



−0.2310 − 0.0957i  
−0.2310 − 0.0957i



−0.1389 + 0.2079i  
−0.1389 + 0.2079i



0.2500
−0.2500  



0.0488 − 0.2452i
−0.0488 + 0.2452i



−0.2310 − 0.0957i  
  0.2310 + 0.0957i



−0.1389 + 0.2079i  
  0.1389 − 0.2079i







ans(:, :, 13, 7) =










0.2500
0.2500



0.1389 − 0.2079i
  0.1389 − 0.2079i



−0.0957 − 0.2310i  
−0.0957 − 0.2310i



−0.2452 − 0.0488i  
−0.2452 − 0.0488i



0.2500
−0.2500  



0.1389 − 0.2079i
−0.1389 + 0.2079i



−0.0957 − 0.2310i  
  0.0957 + 0.2310i



−0.2452 − 0.0488i  
  0.2452 + 0.0488i







ans(:, :, 14, 7) =










0.2500
0.2500



0.2079 − 0.1389i
  0.2079 − 0.1389i



0.0957 − 0.2310i
  0.0957 − 0.2310i



−0.0488 − 0.2452i  
−0.0488 − 0.2452i



0.2500
−0.2500  



0.2079 − 0.1389i
−0.2079 + 0.1389i



0.0957 − 0.2310i
−0.0957 + 0.2310i



−0.0488 − 0.2452i  
  0.0488 + 0.2452i







ans(:, :, 15, 7) =










0.2500
0.2500



0.2452 − 0.0488i
  0.2452 − 0.0488i



0.2310 − 0.0957i
  0.2310 − 0.0957i



0.2079 − 0.1389i
  0.2079 − 0.1389i



0.2500
−0.2500  



0.2452 − 0.0488i
−0.2452 + 0.0488i



0.2310 − 0.0957i
−0.2310 + 0.0957i



0.2079 − 0.1389i
−0.2079 + 0.1389i







ans(:, :, 16, 7) =










0.2500
0.2500



0.2452 + 0.0488i
  0.2452 + 0.0488i



0.2310 + 0.0957i
  0.2310 + 0.0957i



0.2079 + 0.1389i
  0.2079 + 0.1389i



0.2500
−0.2500  



0.2452 + 0.0488i
−0.2452 − 0.0488i



0.2310 + 0.0957i
−0.2310 − 0.0957i



0.2079 + 0.1389i
−0.2079 − 0.1389i










(2) For Rank 4:
For example, the subset of the first codebook may include ans(;,;,n=1), ans(;,;,n=2), ans(;,;,n=3), and ans(;,;,n=4) for rank 4 that are described above.
The subset of the second codebook may include (;,;, n=1), (;,;, n=3), (;,;, n=5), and (;,;, n=7) that are described above.
The combination of the first precoding matrix indicator selected from the subset of the first codebook and the second precoding matrix indicator selected from the subset of the second codebook may indicate one of precoding matrix candidates disclosed in the following overall codebook.












ans(:, :, 1, 1) =










0.1768
0.1768
0.1768
0.1768


0.1768
0.0000 + 0.1768i
0.1768
0.0000 + 0.1768i


0.1768
−0.1768 + 0.0000i  
0.1768
−0.1768 + 0.0000i  


0.1768
−0.0000 − 0.1768i  
0.1768
−0.0000 − 0.1768i  


0.1768
0.1768
−0.1768  
−0.1768  


0.1768
0.0000 + 0.1768i
−0.1768  
−0.0000 − 0.1768i  


0.1768
−0.1768 + 0.0000i  
−0.1768  
0.1768 − 0.0000i


0.1768
−0.0000 − 0.1768i  
−0.1768  
0.0000 + 0.1768i







ans(:, :, 2, 1) =










0.1768
0.1768
0.1768
0.1768


   0 + 0.1768i
−0.1768 + 0.0000i  
   0 + 0.1768i
−0.1768 + 0.0000i  


−0.1768  
0.1768 − 0.0000i
−0.1768  
0.1768 − 0.0000i


   0 − 0.1768i
−0.1768 + 0.0000i  
   0 − 0.1768i
−0.1768 + 0.0000i  


0.1768
0.1768
−0.1768  
−0.1768  


   0 + 0.1768i
−0.1768 + 0.0000i  
   0 − 0.1768i
0.1768 − 0.0000i


−0.1768  
0.1768 − 0.0000i
0.1768
−0.1768 + 0.0000i  


   0 − 0.1768i
−0.1768 + 0.0000i  
   0 + 0.1768i
0.1768 − 0.0000i







ans(:, :, 3, 1) =










0.1768
0.1768
0.1768
0.1768


−0.1768  
−0.0000 − 0.1768i  
−0.1768  
−0.0000 − 0.1768i  


0.1768
−0.1768 + 0.0000i  
0.1768
−0.1768 + 0.0000i  


−0.1768  
0.0000 + 0.1768i
−0.1768  
0.0000 + 0.1768i


0.1768
0.1768
−0.1768  
−0.1768  


−0.1768  
−0.0000 − 0.1768i  
0.1768
0.0000 + 0.1768i


0.1768
−0.1768 + 0.0000i  
−0.1768  
0.1768 − 0.0000i


−0.1768  
0.0000 + 0.1768i
0.1768
−0.0000 − 0.1768i  







ans(:, :, 4, 1) =










0.1768
0.1768
0.1768
0.1768


   0 − 0.1768i
0.1768 − 0.0000i
   0 − 0.1768i
0.1768 − 0.0000i


−0.1768  
0.1768 − 0.0000i
−0.1768  
0.1768 − 0.0000i


   0 + 0.1768i
0.1768 − 0.0000i
   0 + 0.1768i
0.1768 − 0.0000i


0.1768
0.1768
−0.1768  
−0.1768  


   0 − 0.1768i
0.1768 − 0.0000i
   0 + 0.1768i
−0.1768 + 0.0000i  


−0.1768
0.1768 − 0.0000i
0.1768
−0.1768 + 0.0000i  


   0 + 0.1768i
0.1768 − 0.0000i
   0 − 0.1768i
−0.1768 + 0.0000i  







ans(:, :, 1, 3) =










0.1768
0.1768
0.1768
0.1768


0.1633 + 0.0676i
−0.0676 + 0.1633i  
0.1633 + 0.0676i
−0.0676 + 0.1633i  


0.1250 + 0.1250i
−0.1250 − 0.1250i  
0.1250 + 0.1250i
−0.1250 − 0.1250i  


0.0676 + 0.1633i
0.1633 − 0.0676i
0.0676 + 0.1633i
0.1633 − 0.0676i


0.1768
0.1768
−0.1768  
−0.1768  


0.1633 + 0.0676i
−0.0676 + 0.1633i  
−0.1633 − 0.0676i  
0.0676 − 0.1633i


0.1250 + 0.1250i
−0.1250 − 0.1250i  
−0.1250 − 0.1250i  
0.1250 + 0.1250i


0.0676 + 0.1633i
0.1633 − 0.0676i
−0.0676 − 0.1633i  
−0.1633 + 0.0676i  







ans(:, :, 2, 3) =










0.1768
0.1768
0.1768
0.1768


−0.0676 + 0.1633i  
−0.1633 − 0.0676i  
−0.0676 + 0.1633i  
−0.1633 − 0.0676i  


−0.1250 − 0.1250i  
0.1250 + 0.1250i
−0.1250 − 0.1250i  
0.1250 + 0.1250i


0.1633 − 0.0676i
−0.0676 − 0.1633i  
0.1633 − 0.0676i
−0.0676 − 0.1633i  


0.1768
0.1768
−0.1768  
−0.1768  


−0.0676 + 0.1633i  
−0.1633 − 0.0676i  
0.0676 − 0.1633i
0.1633 + 0.0676i


−0.1250 − 0.1250i  
0.1250 + 0.1250i
0.1250 + 0.1250i
−0.1250 − 0.1250i  


0.1633 − 0.0676i
−0.0676 − 0.1633i  
−0.1633 + 0.0676i  
0.0676 + 0.1633i







ans(:, :, 3, 3) =










0.1768
0.1768
0.1768
0.1768


−0.1633 − 0.0676i  
0.0676 − 0.1633i
−0.1633 − 0.0676i  
0.0676 − 0.1633i


0.1250 + 0.1250i
−0.1250 − 0.1250i  
0.1250 + 0.1250i
−0.1250 − 0.1250i  


−0.0676 − 0.1633i
−0.1633 + 0.0676i  
−0.0676 − 0.1633i  
−0.1633 + 0.0676i  


0.1768
0.1768
−0.1768  
−0.1768  


−0.1633 − 0.0676i  
0.0676 − 0.1633i
0.1633 + 0.0676i
−0.0676 + 0.1633i  


0.1250 + 0.1250i
−0.1250 − 0.1250i  
−0.1250 − 0.1250i  
0.1250 + 0.1250i


−0.0676 − 0.1633i  
−0.1633 + 0.0676i  
0.0676 + 0.1633i
0.1633 − 0.0676i







ans(:, :, 4, 3) =










0.1768
0.1768
0.1768
0.1768


0.0676 − 0.1633i
0.1633 + 0.0676i
0.0676 − 0.1633i
0.1633 + 0.0676i


−0.1250 − 0.1250i  
0.1250 + 0.1250i
−0.1250 − 0.1250i  
0.1250 + 0.1250i


−0.1633 + 0.0676i  
0.0676 + 0.1633i
−0.1633 + 0.0676i  
0.0676 + 0.1633i


0.1768
0.1768
−0.1768  
−0.1768  


0.0676 − 0.1633i
0.1633 + 0.0676i
−0.0676 + 0.1633i  
−0.1633 − 0.0676i  


−0.1250 − 0.1250i  
0.1250 + 0.1250i
0.1250 + 0.1250i
−0.1250 − 0.1250i  


−0.1633 + 0.0676i  
0.0676 + 0.1633i
0.1633 − 0.0676i
−0.0676 − 0.1633i  







ans(:, :, 1, 5) =










0.1768
0.1768
0.1768
0.1768


0.1250 + 0.1250i
−0.1250 + 0.1250i  
0.1250 + 0.1250i
−0.1250 + 0.1250i  


0.0000 + 0.1768i
−0.0000 − 0.1768i  
0.0000 + 0.1768i
−0.0000 − 0.1768i  


−0.1250 + 0.1250i  
0.1250 + 0.1250i
−0.1250 + 0.1250i  
0.1250 + 0.1250i


0.1768
0.1768
−0.1768  
−0.1768  


0.1250 + 0.1250i
−0.1250 + 0.1250i  
−0.1250 − 0.1250i  
0.1250 − 0.1250i


0.0000 + 0.1768i
−0.0000 − 0.1768i  
−0.0000 − 0.1768i  
0.0000 + 0.1768i


−0.1250 + 0.1250i  
0.1250 + 0.1250i
0.1250 − 0.1250i
−0.1250 − 0.1250i  







ans(:, :, 2, 5) =










0.1768
0.1768
0.1768
0.1768


−0.1250 + 0.1250i  
−0.1250 − 0.1250i  
−0.1250 + 0.1250i  
−0.1250 − 0.1250i  


−0.0000 − 0.1768i  
0.0000 + 0.1768i
−0.0000 − 0.1768i  
0.0000 + 0.1768i


0.1250 + 0.1250i
0.1250 − 0.1250i
0.1250 + 0.1250i
0.1250 − 0.1250i


0.1768
0.1768
−0.1768  
−0.1768  


−0.1250 + 0.1250i  
−0.1250 − 0.1250i  
0.1250 − 0.1250i
0.1250 + 0.1250i


−0.0000 − 0.1768i  
0.0000 + 0.1768i
0.0000 + 0.1768i
−0.0000 − 0.1768i  


0.1250 + 0.1250i
0.1250 − 0.1250i
−0.1250 − 0.1250i  
−0.1250 + 0.1250i  







ans(:, :, 3, 5) =










0.1768
0.1768
0.1768
0.1768


−0.1250 − 0.1250i  
0.1250 − 0.1250i
−0.1250 − 0.1250i  
0.1250 − 0.1250i


0.0000 + 0.1768i
−0.0000 − 0.1768i  
0.0000 + 0.1768i
−0.0000 − 0.1768i  


0.1250 − 0.1250i
−0.1250 − 0.1250i  
0.1250 − 0.1250i
−0.1250 − 0.1250i  


0.1768
0.1768
−0.1768  
−0.1768  


−0.1250 − 0.1250i  
0.1250 − 0.1250i
0.1250 + 0.1250i
−0.1250 + 0.1250i  


0.0000 + 0.1768i
−0.0000 − 0.1768i  
−0.0000 − 0.1768i  
0.0000 + 0.1768i


0.1250 − 0.1250i
−0.1250 − 0.1250i  
−0.1250 + 0.1250i  
0.1250 + 0.1250i







ans(:, :, 4, 5) =










0.1768
0.1768
0.1768
0.1768


0.1250 − 0.1250i
0.1250 + 0.1250i
0.1250 − 0.1250i
0.1250 + 0.1250i


−0.0000 − 0.1768i  
0.0000 + 0.1768i
−0.0000 − 0.1768i  
0.0000 + 0.1768i


−0.1250 − 0.1250i  
−0.1250 + 0.1250i  
−0.1250 − 0.1250i  
−0.1250 + 0.1250i  


0.1768
0.1768
−0.1768  
−0.1768  


0.1250 − 0.1250i
0.1250 + 0.1250i
−0.1250 + 0.1250i  
−0.1250 − 0.1250i  


−0.0000 − 0.1768i  
0.0000 + 0.1768i
0.0000 + 0.1768i
−0.0000 − 0.1768i  


−0.1250 − 0.1250i  
−0.1250 + 0.1250i  
0.1250 + 0.1250i
0.1250 − 0.1250i







ans(:, :, 1, 7) =










0.1768
0.1768
0.1768
0.1768


0.0676 + 0.1633i
−0.1633 + 0.0676i  
0.0676 + 0.1633i
−0.1633 + 0.0676i  


−0.1250 + 0.1250i  
0.1250 − 0.1250i
−0.1250 + 0.1250i  
0.1250 − 0.1250i


−0.1633 − 0.0676i  
−0.0676 + 0.1633i  
−0.1633 − 0.0676i  
−0.0676 + 0.1633i  


0.1768
0.1768
−0.1768  
−0.1768  


0.0676 + 0.1633i
−0.1633 + 0.0676i  
−0.0676 − 0.1633i  
0.1633 − 0.0676i


−0.1250 + 0.1250i  
0.1250 − 0.1250i
0.1250 − 0.1250i
−0.1250 + 0.1250i  


−0.1633 − 0.0676i  
−0.0676 + 0.1633i  
0.1633 + 0.0676i
0.0676 − 0.1633i







ans(:, :, 2, 7) =










0.1768
0.1768
0.1768
0.1768


−0.1633 + 0.0676i  
−0.0676 − 0.1633i  
−0.1633 + 0.0676i  
−0.0676 − 0.1633i  


0.1250 − 0.1250i
−0.1250 + 0.1250i  
0.1250 − 0.1250i
−0.1250 + 0.1250i  


−0.0676 + 0.1633i  
0.1633 + 0.0676i
−0.0676 + 0.1633i  
0.1633 + 0.0676i


0.1768
0.1768
−0.1768  
−0.1768  


−0.1633 + 0.0676i  
−0.0676 − 0.1633i  
0.1633 − 0.0676i
0.0676 + 0.1633i


0.1250 − 0.1250i
−0.1250 + 0.1250i  
−0.1250 + 0.1250i  
0.1250 − 0.1250i


−0.0676 + 0.1633i  
0.1633 + 0.0676i
0.0676 − 0.1633i
−0.1633 − 0.0676i  







ans(:, :, 3, 7) =










0.1768
0.1768
0.1768
0.1768


−0.0676 − 0.1633i  
0.1633 − 0.0676i
−0.0676 − 0.1633i  
0.1633 − 0.0676i


−0.1250 + 0.1250i  
0.1250 − 0.1250i
−0.1250 + 0.1250i  
0.1250 − 0.1250i


0.1633 + 0.0676i
0.0676 − 0.1633i
0.1633 + 0.0676i
0.0676 − 0.1633i


0.1768
0.1768
−0.1768  
−0.1768  


−0.0676 − 0.1633i  
0.1633 − 0.0676i
0.0676 + 0.1633i
−0.1633 + 0.0676i  


−0.1250 + 0.1250i  
0.1250 − 0.1250i
0.1250 − 0.1250i
−0.1250 + 0.1250i  


0.1633 + 0.0676i
0.0676 − 0.1633i
−0.1633 − 0.0676i  
−0.0676 + 0.1633i  







ans(:, :, 4, 7) =










0.1768
0.1768
0.1768
0.1768


0.1633 − 0.0676i
0.0676 + 0.1633i
0.1633 − 0.0676i
0.0676 + 0.1633i


0.1250 − 0.1250i
−0.1250 + 0.1250i  
0.1250 − 0.1250i
−0.1250 + 0.1250i  


0.0676 − 0.1633i
−0.1633 − 0.0676i  
0.0676 − 0.1633i
−0.1633 − 0.0676i  


0.1768
0.1768
−0.1768  
−0.1768  


0.1633 − 0.0676i
0.0676 + 0.1633i
−0.1633 + 0.0676i  
−0.0676 − 0.1633i  


0.1250 − 0.1250i
−0.1250 + 0.1250i  
−0.1250 + 0.1250i  
0.1250 − 0.1250i  


0.0676 − 0.1633i
−0.1633 − 0.0676i  
−0.0676 + 0.1633i  
0.1633 + 0.0676i  









FIG. 6 illustrates an example of a communication method of a transmitter and a receiver that operate in PUCCH 2-1 sub-modes 1 and 2.
At 610, the transmitter and the receiver may determine a subset of a first codebook and a subset of a second codebook that are described above. The subset of the first codebook and the subset of the second codebook may be individually stored in the transmitter and the receiver. The overall codebook in which the subset of the first codebook and the subset of the second codebook are integrated may be stored in the transmitter and the receiver.
At 621, the receiver may determine PTI as ‘0’. At 622, the receiver may feed back PTI=0 to the transmitter. At 631, the receiver may extract a first precoding matrix indicator from the subset of the first codebook. When a point in time when the receiver feeds back a precoding matrix indicator is a first reporting point in time in PTI=0, the receiver may feed back the first precoding matrix indicator to the transmitter at the first reporting point in time at 632. CQI, a rank indicator, and the like may be further fed back.
At 640, the transmitter may generate W based on the first precoding matrix indicator, and perform precoding using W and transmit data. While PTI=0, the aforementioned process may be repeated.
When the receiver determines PTI=1 at 651, the receiver may feed back PTI=1 to the transmitter at 652. At 661, the receiver may extract a second precoding matrix indicator from the subset of the second codebook. When a point in time when the receiver feeds back a precoding matrix indicator is a second reporting point in time in PTI=0, the receiver may feed back the second precoding matrix indicator to the transmitter at the second reporting point in time at 662. CQI, a rank indicator, and the like may be further fed back.
At 670, the transmitter may generate W based on the second precoding matrix indicator, and perform precoding using W and transmit data. The transmitter may generate new W by updating the second precoding matrix indicator based on the previously used W. While PTI=0, the aforementioned process may be repeated.
A number of examples have been described above. Nevertheless, it should be understood that various modifications may be made. For example, suitable results may be achieved if the described techniques are performed in a different order and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Accordingly, other implementations are within the scope of the following claims.

## Claims

1. A communication method of a receiver in a wireless communication system, the communication method comprising:
obtaining a rank indicator;
obtaining a first precoding matrix indicator based on the rank indicator;
obtaining a second precoding matrix indicator associated with the first precoding matrix indicator;
when the rank indicator is 1,
transmitting the rank indicator,
transmitting the first precoding matrix indicator obtained based on a subset {0, 2, 4, 6, 8, 10, 12, 14} of a first codebook, the second precoding matrix indicator and a wideband channel quality index (CQI); and

when the rank indicator is 2,
transmitting the rank indicator, and
transmitting the first precoding matrix indicator obtained based on a subset {0, 2, 4, 6, 8, 10, 12, 14} of the first codebook, the second precoding matrix indicator and a wideband channel quality index(CQI),

wherein when the rank indicator is 1 or 2, the first precoding matrix indicator is 3 bits, and the second precoding matrix indicator is 1 bit.

2. The communication method of claim 1, wherein a combination of the first precoding matrix indicator and the second precoding matrix indicator indicates a single recommended precoding matrix.

3. The communication method of claim 1, wherein a combination of the first precoding matrix indicator and the second precoding matrix indicator indicates one of recommended precoding matrix candidates disclosed in the following Table 1:










TABLE 1









W(1)0,0
W(1)0,2



W(1)4,0
W(1)4,2



W(1)8,0
W(1)8,2



W(1)12,0
W(1)12,2



W(1)16,0
W(1)16,2



W(1)20,0
W(1)20,2



W(1)24,0
W(1)24,2



W(1)28,0
W(1)28,2









wherein





  
    
      W
      
        m
        ,
        n
      
      
        (
        1
        )
      
    
    =
    
      
        1
        
          8
        
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.

4. The communication method of claim 1, wherein a combination of the first precoding matrix indicator and the second precoding matrix indicator indicates one of recommended precoding matrix candidates disclosed in the following Table 2:










TABLE 2









W(2)0,0,0
W(2)0,0,1



W(2)4,4,0
W(2)4,4,1



W(2)8,8,0
W(2)8,8,1



W(2)12,12,0
W(2)12,12,1



W(2)16,16,0
W(2)16,16,1



W(2)20,20,0
W(2)20,20,1



W(2)24,24,0
W(2)24,24,1



W(2)28,28,0
W(2)28,28,1









wherein





  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        2
        )
      
    
    =
    
      
        1
        4
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.

5. The communication method of claim 1, wherein a physical uplink control channel (PUCCH) mode is corresponding to 1-1.

6. The communication method of claim 1, further comprising:
when the rank indicator is 3,
transmitting the rank indicator, and
transmitting the first precoding matrix indicator obtained based on a subset {0, 2} of the first codebook, the second precoding matrix indicator and a wideband channel quality index(CQI),

wherein when the rank indicator is 3, the first precoding matrix indicator is 1 bit, and the second precoding matrix indicator is 3 bits.

7. The communication method of claim 1, further comprising:
when the rank indicator is 5 or 6,
transmitting the rank indicator, and
transmitting the first precoding matrix indicator obtained based on a subset {0, 1, 2, 3} of the first codebook, the second precoding matrix indicator and a wideband channel quality index(CQI),

wherein when the rank indicator is 5 or 6, the first precoding matrix indicator is 2 bits, and the second precoding matrix indicator is 0 bit.

8. A communication method of a receiver in a multiple input multiple output (MIMO) communication system, the communication method comprising:
feeding back, to a transmitter, a first precoding matrix indicator corresponding to a first codeword index included in a first codebook in order to indicate a recommended precoding matrix at a first reporting point; and
feeding back, to the transmitter, a second precoding matrix indicator corresponding to a second codeword index included in a second codebook in order to indicate a recommended precoding matrix at a second reporting point,
wherein the second precoding matrix indicator indicates, as the recommended precoding matrix at the second reporting point, one of candidates disclosed in the following Table 3:











TABLE 3









W(2)0,0,0
W(2)2,2,0



W(2)2,2,0
W(2)4,4,0



W(2)4,4,0
W(2)6,6,0



W(2)6,6,0
W(2)8,8,0



W(2)8,8,0
W(2)10,10,0



W(2)10,10,0
W(2)12,12,0



W(2)12,12,0
W(2)14,14,0



W(2)14,14,0
W(2)16,16,0



W(2)16,16,0
W(2)18,18,0



W(2)18,18,0
W(2)20,20,0



W(2)20,20,0
W(2)22,22,0



W(2)22,22,0
W(2)24,24,0



W(2)24,24,0
W(2)26,26,0



W(2)26,26,0
W(2)28,28,0



W(2)28,28,0
W(2)30,30,0



W(2)30,30,0
W(2)0,0,0



W(2)1,1,0
W(2)3,3,0



W(2)3,3,0
W(2)5,5,0



W(2)5,5,0
W(2)7,7,0



W(2)7,7,0
W(2)9,9,0



W(2)9,9,0
W(2)11,11,0



W(2)11,11,0
W(2)13,13,0



W(2)13,13,0
W(2)15,15,0



W(2)15,15,0
W(2)17,17,0



W(2)17,17,0
W(2)19,19,0



W(2)19,19,0
W(2)21,21,0



W(2)21,21,0
W(2)23,23,0



W(2)23,23,0
W(2)25,25,0



W(2)25,25,0
W(2)27,27,0



W(2)27,27,0
W(2)29,29,0



W(2)29,29,0
W(2)31,31,0



W(2)31,31,0
W(2)1,1,0









wherein





  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        2
        )
      
    
    =
    
      
        1
        4
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.

9. A communication method of a receiver in a multiple input multiple output (MIMO) communication system, the communication method comprising:
feeding back, to a transmitter, a first precoding matrix indicator corresponding to a first codeword index included in a first codebook in order to indicate a recommended precoding matrix at a first reporting point; and
feeding back, to the transmitter, a second precoding matrix indicator corresponding to a second codeword index included in a second codebook in order to indicate a recommended precoding matrix at a second reporting point,
wherein the second precoding matrix indicator indicates, as the recommended precoding matrix at the second reporting point, one of candidates disclosed in the following Table 4:












TABLE 4










W(4)0,8,0





W(4)8,16,0





W(4)16,24,0





W(4)24,32,0





W(4)2,10,0





W(4)10,18,0





W(4)18,26,0





W(4)26,34,0





W(4)4,12,0





W(4)12,20,0





W(4)20,28,0





W(4)28,36,0





W(4)6,14,0





W(4)14,22,0





W(4)22,30,0





W(4)30,38,0









wherein





  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        4
        )
      
    
    =
    
      
        1
        
          32
        
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.

10. A communication method of a transmitter in a multiple input multiple output (MIMO) communication system, the communication method comprising:
receiving, from a receiver, a first precoding matrix indicator corresponding to a first codeword index included in a first codebook and a second precoding matrix indicator corresponding to a second codeword index included in a second codebook; and
obtaining a precoding matrix based on the first precoding matrix indicator and the second precoding matrix indicator,
wherein a combination of the first precoding matrix indicator and the second precoding matrix indicator indicates one of recommended precoding matrix candidates disclosed in one of the following Table 5 and Table 6:











TABLE 5









W(1)0,0
W(1)0,2



W(1)4,0
W(1)4,2



W(1)8,0
W(1)8,2



W(1)12,0
W(1)12,2



W(1)16,0
W(1)16,2



W(1)20,0
W(1)20,2



W(1)24,0
W(1)24,2



W(1)28,0
W(1)28,2









wherein





  
    
      W
      
        m
        ,
        n
      
      
        (
        1
        )
      
    
    =
    
      
        1
        
          8
        
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T










TABLE 6









W(2)0,0,0
W(2)0,0,1



W(2)4,4,0
W(2)4,4,1



W(2)8,8,0
W(2)8,8,1



W(2)12,12,0
W(2)12,12,1



W(2)16,16,0
W(2)16,16,1



W(2)20,20,0
W(2)20,20,1



W(2)24,24,0
W(2)24,24,1



W(2)28,28,0
W(2)28,28,1









wherein





  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        2
        )
      
    
    =
    
      
        1
        4
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.

11. A communication method of a transmitter in a multiple input multiple output (MIMO) communication system, the communication method comprising:
receiving, from a receiver, a first precoding matrix indicator corresponding to a first codeword index included in a first codebook, the first precoding matrix indicator indicating a recommended precoding matrix at a first reporting point;
receiving, from the receiver, a second precoding matrix indicator corresponding to a second codeword index included in a second codebook, the second precoding matrix indicator indicating a recommended precoding matrix at a second reporting point; and
obtaining the recommended precoding matrix at the second reporting point based on the second precoding matrix indicator received at the second reporting point,
wherein the second precoding matrix indicator indicates, as the recommended precoding matrix at the second reporting point, one of recommended precoding matrix candidates disclosed in one of the following Table 3 and Table 4:











TABLE 3









W(2)0,0,0
W(2)2,2,0



W(2)2,2,0
W(2)4,4,0



W(2)4,4,0
W(2)6,6,0



W(2)6,6,0
W(2)8,8,0



W(2)8,8,0
W(2)10,10,0



W(2)10,10,0
W(2)12,12,0



W(2)12,12,0
W(2)14,14,0



W(2)14,14,0
W(2)16,16,0



W(2)16,16,0
W(2)18,18,0



W(2)18,18,0
W(2)20,20,0



W(2)20,20,0
W(2)22,22,0



W(2)22,22,0
W(2)24,24,0



W(2)24,24,0
W(2)26,26,0



W(2)26,26,0
W(2)28,28,0



W(2)28,28,0
W(2)30,30,0



W(2)30,30,0
W(2)0,0,0



W(2)1,1,0
W(2)3,3,0



W(2)3,3,0
W(2)5,5,0



W(2)5,5,0
W(2)7,7,0



W(2)7,7,0
W(2)9,9,0



W(2)9,9,0
W(2)11,11,0



W(2)11,11,0
W(2)13,13,0



W(2)13,13,0
W(2)15,15,0



W(2)15,15,0
W(2)17,17,0



W(2)17,17,0
W(2)19,19,0



W(2)19,19,0
W(2)21,21,0



W(2)21,21,0
W(2)23,23,0



W(2)23,23,0
W(2)25,25,0



W(2)25,25,0
W(2)27,27,0



W(2)27,27,0
W(2)29,29,0



W(2)29,29,0
W(2)31,31,0



W(2)31,31,0
W(2)1,1,0









wherein





  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        2
        )
      
    
    =
    
      
        1
        4
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T











TABLE 4










W(4)0,8,0





W(4)8,16,0





W(4)16,24,0





W(4)24,32,0





W(4)2,10,0





W(4)10,18,0





W(4)18,26,0





W(4)26,34,0





W(4)4,12,0





W(4)12,20,0





W(4)20,28,0





W(4)28,36,0





W(4)6,14,0





W(4)14,22,0





W(4)22,30,0





W(4)30,38,0










wherein




  
    
      W
      
        m
        ,
        
          m
          ′
        
        ,
        n
      
      
        (
        4
        )
      
    
    =
    
      
        1
        
          32
        
      
      ⁡
      
        [
        
          
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
            
              
                v
                m
              
            
            
              
                v
                
                  m
                  ′
                
              
            
          
          
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  φ
                  n
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  m
                
              
            
            
              
                
                  -
                  
                    φ
                    n
                  
                
                ⁢
                
                  v
                  
                    m
                    ′
                  
                
              
            
          
        
        ]
      
    
  
  ,
  
    
      φ
      n
    
    =
    
      e
      
        j
        ⁢
        
          
        
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          n
          /
          2
        
      
    
  
  ,




and νm=[1 ej2πn/32 ej4πn/32 ej6πn/32]T, and
wherein W denotes a precoding matrix, v denotes a column vector, and m and n are variables.